high density plasma in black hole candidates_aps_aprilmeeting_92008

Ari Brynjolfsson: High Density Plasmas in Black Hole Candidates 1

High Density Plasmas in Black Hole Candidates

Ari Brynjolfsson ∗

Applied Radiation Industries, 7 Bridle Path, Wayland, MA 01778, USA

Abstract

While cosmological observations are progressing exceptionally well, the theoretical interpre-tation of the observations are becoming ever more difficult. The difficulties are mainly due totwo fundamental misconceptions: 1. It is generally believed that most of the redshifts are due toDoppler shifts, while in fact most of them are due to plasma redshifts. 2. It is generally believedthat photons have weight in the local system of reference, while photons actually are weightless.Eliminating these misconceptions changes in fundamental ways the cosmological perspectiveand facilitates explanation of great many phenomena that have been difficult to explain, in-cluding the physics of black hole candidates. The overlooked plasma-redshift cross-section givesan explanation of the cosmological redshift without big bang, inflation, dark energy, or darkmatter. It also explains the cosmic microwave background, the X-ray background, and muchmore. There are no black holes due to the weightlessness of photons. Instead the black holecandidates are engines for conversion of burned out nuclear matter to hot and dense primordialmatter, which assures continual renewal of the world.

Keywords: Big-bang cosmology, plasma-redshift cosmology, primordial plasma, high density plasma,nucleosynthesis, cosmological redshift, plasma redshift, cosmic evolution, dark energy, dark matter,black hole, black hole candidates.PACS: 52.25.Os, 52.40.-w, 98.80.Es

1 Introduction

The discovery of the plasma-redshift cross-section for photons’ interactions with hot sparse plasmarevolutionizes the cosmological perspective; see [1]. This interaction explains: a) the cosmologicalredshifts; b) the magnitude redshift relation for SNe Ia without the use of Dark Energy, Dark Matter,or cosmic time dilation, and without Big Bang or any expansion of the universe; c) the heating of therelatively hot, T ≈ 2.7 · 106 K, and dense, Ne ≈ 2 · 10−4 cm−3, intergalactic plasma; d) the cosmicmicrowave background with black body temperature of T ≈ 2.73 K; e) the X-ray background; andf) many phenomena around black hole candidates (BHC), including regeneration of old star matter,the main subject of this article.

In case of fast charged particles interactions with matter, great many authors have contributedto the our understanding. Most outstanding of these are: a) Niels Bohr’s classical treatment fornon-relativistic particles [2], and [3], and his extension of these calculations to relativistic particles[4]; b) Hans Bethe’s quantum mechanical treatment of the interaction of non-relativistic incidentparticles [5]; c) Christian Møller’s relativistic extension of Bethe’s calculations [6] and [7]; and d)Enrico Fermi’s treatment of the interactions of incident charged particles with ponderable matter in1939 [8] and in 1940 [9]. In the context of plasma redshift of photons, these Fermi’s contributions areespecially important, because until then the interactions had focused mainly on interactions withindividual atoms; but Fermi took into account the density effect and collective interactions withmatter. He did this by taking into account the importance of the dielectric constant. Before thesepapers by Enrico Fermi, it was not possible to explain the Cerenkov radiation, which had been a

∗Corresponding author: [email protected]


mystery for many years. Later, others contributed to the theory of this density effect (also calledpolarization effect); see [10], [11], and [12].

In case of incident photons interactions with matter, the primary focus is usually on the photo-electric effect, Raman effect, and on many scattering effects, including Compton scattering, andRayleigh scattering and several other coherent effects. Often, these effects are treated quantummechanically, but also semi-classically. A good deduction and review of the many interactions ofphotons with matter is given by Heitler [13]. Heitler’s monograph includes also a good quantummechanical treatment of the double and multiple Compton scattering. These interactions deal withone incident photon and two or more outgoing photons, as opposed to only one outgoing photonin the conventional Compton scattering. The double and multiple Compton scattering are purelyquantum mechanical effects. Heitler managed to treat accurately the infinity problem in case oneof the outgoing photon is very soft. He found the integral of this cross section to be finite and onlyabout 1/137 of that in the Compton scattering. However, Heitler only treated the interaction withindividual electrons, and disregarded collective effects. This was reasonable, because in laboratoryexperiment the density effects are insignificant. However, the density effect, which results in theplasma redshift of photons, is very significant in the large dimensions of a hot sparse plasma, such asthat in the corona of the Sun, stars, and galaxies, and in the hot sparse plasma of intergalactic space.Heitler’s omission of the density effect in case of photons is comparable to the omission of the densityeffect (resulting in Cerenkov radiation) in the treatment of fast charged particles interactions beforeFermi’s articles in 1939 [8] and 1940 [9] that were essential for explaining the Cerenkov radiation.

For deriving the plasma redshift, it is essential to treat the electromagnetic spectrum as consistingof quantum mechanical photons. Each photon in turn is composed of Fourier components given bythe well known Lorentzian distribution. It is also essential to take the dielectric constant, or thepolarization into account.

The dielectric constant in the equation of motion (see Eq.(A12) of Apendix A in [1]) is usuallyequated with one. This is permissible in laboratory experiments. But in hot sparse plasma ofintergalactic space, this approximation is not permissible. It is essential to use the correct dielectricconstant and its variations with the frequency of the Fourier harmonics for the photon; and itis necessary to integrate the attenuation of the photon energy more exactly than is usual in theconventional literature. When this is done, the integration of the photon’s attenuation in hot sparseplasma results in the plasma-redshift cross section in addition to the conventionally known crosssections for photoelectric effect, the Compton scattering and the Raman scattering on theplasma frequency. Although this Raman scattering on the plasma frequency has not been consideredbefore, I considered it as conventional, because the Raman scattering is well known.

2 The relation between plasma-redshift and density

Plasma-redshift is not a suggestion, a proposal, a model, or a hypothesis; instead, it is theoreticallydeduced (just like Compton scattering) in accordance with well-established conventional laws ofphysics. However, because it is newly discovered cross section, it is of interest to compare itspredictions with the results of experiments. The plasma redshift is proportional to the electrondensity integrated along the photon-track from the object to the observer at a distance R from theobject. We have:

ln(1 + z) = 3.326 · 10−25

∫ R

0

Ne dx +γi − γ0

ξ ω, (1)

where Ne is the electron density in cm−3 and x is in cm. The initial quantum mechanical photonwidth γi includes the initial pressure and Stark broadening. The photon width refers to the half-width at half maximum in the Lorentz distribution for the line intensity. Lorentz distribution is thesame as the Breit-Wigner distribution in nuclear physics or Cauchy distribution in mathematics andstatistics. In the Sun, the Lorentzian form of the line dominates the Gaussian form of the line beyondabout three half-widths. This has been used for experimental determination of the Lorentzian widthγi of the solar photons. It is closely related to the decay constant for the transition, and the strengthof the line. The pressure broadening in the line forming elements can also be estimated theoretically.


The classical photon width is γ0 = 2e2ω2/(3mec3) = 6.266 ·10−24 ω2, where ω is the cyclic frequency

of the incident photon. γ0 is about equal to the quantum mechanical width of photons that havepassed through a hot sparse plasma with column density exceeding about 5 · 1017 electrons per cm2.

The second term on the right side of Eq. (1) is insignificant when dealing with cosmologicalredshifts. But it is usually significant for the small redshifts in the Sun and most of the stars. Thevariations in the photon width, γi, are due to variations in both the intrinsic photon width and thepressure and Stark broadening of the photon width. The effect of Stark shift is usually insignificant.These variations in turn account for most of the variation of the redshifts of the solar lines from lineto line, including most of the variation in the center to limb effect from line to line. The average ofthe Doppler shifts due to by movements in the line forming elements in the photosphere are nearlyinsignificant. The variations in the intrinsic photon width and the pressure broadening (includingthe Stark broadening) of the photon width, γi, is especially important in collapsars, such as thewhite dwarfs and BHCs. For the resonance lines of sodium and potassium in the Sun, the pressurebroadening is about a factor of 10 greater than the intrinsic photon width, but for strong lines, suchas 630.25 nm Fe-I line, with high excitation potentials the pressure broadenings are small. For thefrequency range of main interest, we have that ξ ≈ 0.25.

Plasma-redshift cut-off relation. The plasma redshift given by Eq. (1) is significant only ifthe plasma densities are very low and the plasma temperatures very high. This cut-off is the mainreason why the plasma redshift was not discovered long time ago. Plasma physicists were usuallydealing with relatively dense and cold laboratory plasmas. Plasma redshift is possible only if thefollowing condition is fulfilled [1]

λ ≤ λ0.5 = 318.5 ·(

1 + 1.3 · 105 B2

Ne

)Te√Ne

A, (2)

where λ is the wavelength of the incident photons in Angstrom units, B is the magnetic field ingauss units, Te is the electron temperature in degrees K, and Ne is the electron density in cm−3.Accordingly, the plasma redshift is not possible in conventional laboratory plasmas or in the reversinglayer and the chromosphere of the Sun, because the densities are too high and the temperatures toolow.

For the shorter wavelengths, λ ≤ λ0.5, of the solar spectrum, the plasma redshift starts low inthe transition zone. For the longer wavelengths, λ ≥ λ0.5, it starts high in the transition zone tothe solar corona. In the middle of the transition zone to a quiescent solar corona the magneticfield is usually on the order of 5 gauss, the temperature about 500,000 K, and the density aboutNe ≈ 109 cm−3. When we insert these values into Eq. (2), we get that the cut-off wavelength forthe plasma redshift is at λ0.5 ≈ 5, 000 A. This means that photons with wavelengths smaller thanλ0.5 = 5, 000 A will be redshifted more than 50 % of the redshift given by Eq. (1); and those withwavelength larger than λ0.5 = 5, 000 A will be redshifted less than 50% of the redshift given byEq. (1).

The distance-redshift relation follows from Eq. (1). In intergalactic space the second term isis usually insignificant. We have then that the distance R to an object is given by; see Eq. (1) of [1]

R =c

H0ln (1 + z) , (3)

where R is in Mpc, c is the velocity of light in km s−1, and H0 is the Hubble constant in km s−1 Mpc−1.The gravitational redshift. When the predicted plasma redshift, based on the known electron

densities and photon widths in the solar corona, was compared with the observed redshifts of thesolar Fraunhofer lines, it became clear that the solar lines are not gravitationally redshifted;see section 5.6.2 and Fig. (4) of [1]. Instead, the redshifts of the solar Fraunhofer lines is due mainlyto the plasma-redshift cross section. I analyzed the many well executed experiments by Pound andRebka, by Pound and Snider, the rocket experiments by Vessot et al., and the space experiments byKrisher et al.; see, Brynjolfsson: Weightlessness of photons: A quantum effect, [14]. The experimentshave been interpreted, incorrectly, to prove the weight of the photons. All the experiments have beendesigned and interpreted as if classical physics ruled the world and not quantum mechanics. Photons


are gravitationally redshifted when they are in the Sun, but during the time of flight from the Sunto the Earth, the frequencies of the photons are blue shifted to cancel the gravitational redshifts.Also the gravitationally redshifted frequencies of atoms (and atomic clocks) are blue shifted whenthe atoms move to the Earth such as to cancel their gravitational redshift. There is, however, adifference. We have to transfer energy to the atom by lifting it up from Sun to Earth. In case ofphotons, they are being repelled by the gravitational field as seen by a distant observer on Earth;that means that the photons are weightless as seen by a local observer.

Quantum mechanics makes it impossible for the photons to change their frequency during theshort time of flight from the emitter to the absorber in these experiments. For example, in Poundand Rebkas experiments the photons time of flight from emitter to absorber was only 22.5/(3 ·108) =7.5 · 10−8 seconds, while according to the uncertainty principle in quantum mechanics at least 250times longer time (or at least 1.9 · 10−5 seconds) is required for the nuclear iron line (of 14.4 keVphoton) to adjust to the difference in gravitational potential. For comparison, the flight of time forphotons moving from the Sun to the Earth lasts about 8.3 minutes while a few times 10−5 secondswould be adequate. The weightlessness of photons does not destroy the general theory of relativity(GTR); it only modifies it; see [14].

The weightlessness of photons is most important for the explanation of the renewal of matter andmany phenomena associated with BHCs. The photons are weightless in a local system of reference(where the observer and the photons are), but repelled in a reference system of distant observer,such as an observer on Earth looking at photon experiments in the Sun. This repulsion of photonscancels the gravitational redshift when the photons emitted in the Sun are observed on Earth. Thisis a remarkable, because it contradicts general opinion.

3 The Black Hole Limit

The weightlessness of photons in the local system of reference eliminates the need for black holes. Theobjects that the big-bang cosmologists call black holes (BHs) or super-massive black holes (SMBHs),such as Sgr A∗ at the center of our Galaxy, we will usually refer to as black hole candidates (BHCs) orsuper-massive black hole candidates (SMBHCs). At the center, the BHCs and SMBHCs have a denseweightless photon ”bubble” that prevents the formation of a black hole and facilitates formation ofvery hot primordial like matter. The photon ”bubble” is surrounded by a layer of quark-gluonplasma, then a neutron layer and layers of very hot and dense proton-electron plasma.

In the general theory of relativity (GTR), the gravitational time dilation and the gravitationalredshift are both given by; see Møller’s Eqs. (8.114), (10.62) and (10.65) in [15]

dt

dτ=

1√(√1− 2 G M/(R c2)− γιuι/c

)2

− u2/c2

= ε = (1 + zgr) =λgr

λ0, (4)

where the proper time τ is the time measured by an observer following the particle; and t is the timemeasured by a distant observer far away from the gravitating body. G = 6.673 · 10−8 cm g−1 s−2

is Newton’s gravitational constant; M is the mass inside R; and u the velocity of the particle atthe position of R from the center of the BHC. ε = (1 + zgr) is the GTR factor replacing theLorentz factor (1− u2/c2)−1/2 in special theory of relativity (STR), and where zgr is the expandedgravitational redshift in big-bang cosmology, which besides the usual gravitational redshift includesthe modification by the particles movements, as given by Eq. (4). λgr is the gravitationally redshiftedwavelength of λ0.

For a non-rotating system, γι = 0, Eq. (4) takes the form dt = dτ/√

1− 2 G M/(R c2)− u2/c2 .For u ≈ 0, we have then that

R > RS ≈2 G M

c2= 1.485 · 10−28 M = 2.95 · 105 M

Mcm . (5)

where RS , the Schwarzschild radius or the radius of a black hole in the big-bang cosmology. It marksthe radius where even light cannot escape. When R approaches this limit, the time increment, dt,


approaches infinity, and the frequency of light approach zero. Close to the RS-limit, we get whenwe multiply Eq. (5) by mc2/RS that

mc2 ≈ 2 G M m

RS, or mc2 − G M m

RS≈ G M m

RS= Ekin = Qheat , (6)

where mc2 = m0c2 +Ekin is the total energy; m0c

2 is the rest energy; and Ekin is the kinetic energyof the particle. If the particle is stopped, the kinetic energy is transformed into Qheat. We see thatmc2 is twice the loss in potential energy, G M m/RS , which is equal to the kinetic energy gained ina free fall. mc2 ≈ 2Ekin, therefore, Ekin is equal to the rest energy of the particle. This assumesthat the particle’s energy loss as it falls towards this limit is negligible. The fusion energy (evenfusion resulting in iron) is an insignificant (less than 1%) part of rest energy.

In Eqs. (4), we may have that the value of u2/c2 approaches 2GM/R′sc

2. The correspondingsingularity is then at the limiting radius of R′ ≈ 2RS . From Eq. (5), we see that any thermal motion,u, causes the limiting radius R′

s to increase well beyond the limiting radius RS . The term with γι inEq. (4) in a rotating system (Kerr black hole), cannot eliminate the increase in Schwarzschild radiuswith u . Also electrical and magnetic fields affect the limiting radius. Due to the thermal motionsand the fields, the radius R′

s has usually a broad distribution.Close to the limiting radius of the BHC, a local observer with a local clock measuring the

time differential dτ sees the environment differently from that of a distant observer on Earth, whomeasures the corresponding time differential dt. To the local observer at R that is only slightlylarger than the limiting radius, the time dτ may be short, the frequency normal, and the temperaturevery high; but a distant observer sees in all cases dt approach infinity and the frequency and thetemperature approach zero. This is true in both the big-bang and the plasma-redshift cosmology.

The gravitational field affects not only time as in Eq. (4), but it affects also the mass, the velocityof light, and the spatial dimensions. All the equations are in plasma-redshift cosmology the sameas the conventional equations. The difference is only in the way the photon frequency varies whenthe photon moves from the gravitating body (such as a BHC) outwards to a distant observer (forexample on the Earth). In plasma-redshift cosmology, the photon frequency increases and cancelsthe gravitational redshift as the photon moves outwards (see section 2.6 above), while accordingto Einstein’s GTR the photon’s gravitationally redshifted frequency stays constant as the photonsmove outwards, for example, from the Sun to the Earth.

The plasma-redshift cosmology accepts the conventional assumptions of physics, which demandthat the time t in Eq. (4) is real at all times. In plasma-redshift cosmology, we cannot, therefore,have a black hole. In the following, we show how the plasma-redshift cosmology can easily deny theexistence of a black hole. In contrast, the big-bang cosmology always results in black holes.

4 Photon Bubble and Hot Plasma at the Center of BHCs

When a star collapses to the BH limit, the kinetic energy of the particles approaches the rest energyof the particles. For example, the kinetic energy of the neutron approaches Ekin ≈ mc2 −m0 c2 ≈m0 c2 ≈ (3/2)kT = 940 MeV. The corresponding temperature is then T ≈ 7.27 · 1012 K. Theseequations apply also in the big-bang cosmology. But in big-bang cosmology it is usually surmisedthat the centers cools down quickly (to about Tp ≤ 1011 K, or Tp ≤ 107 eV, mainly because the hotmatter disappears into the BH). In plasma-redshift cosmology that is not the case, because matterconverts to weightless photons that prevent formation of a black hole. This is all in accordance withconventional laws of physics. Also, in big bang cosmology the emission from the surface of a hotobject is large, while in plasma redshift cosmology the emission from a hot plasma is relatively low.Due to plasma redshift cross section, the black body emission temperature from the outermost hotplasma surrounding the BHCs and SMBHCs is (see section C1.7 of [1]),

aT 4empl = 3 p = 3N k Tp erg cm−3, (7)

and where a = 7.566 · 10−15 and the particle density N consists mainly of protons, helium ions,and electrons. For 10 % helium concentration, we getN ≈ Np + NHe + Ne ≈ 1.917Ne cm−3, From


Eqs. (9), we get that Templ ≈ 0.569 · (Ne Tp)1/4 K. The black-body emission-temperature, Templ,

from the hot plasma surrounding the BHC is usually much smaller than the particle temperature,Tp. The observed frequencies of the emission are often in the microwave and infrared part of thespectrum. The low emission temperature or low luminosity from the surface of SMBHCs has longbeen a mystery. But Eq. (9) gives a physical explanation of this. Sgr A∗ at the center of our Galaxyis the best studied SMBHC and can be used for comparison with experiments.

Plasma-redshift cross-section is most important in sparse hot plasma. But in the deeper layersof BHCs and in SMBHCs the plasma is often dense, and the free-free absorption (and emission)may then become larger than the plasma-redshift absorption (and emission); see section C1.4 inAppendix C of [1]. For example, if the frequency is 1012 and Tp ≈ 108, then fre-free absorption (andemission) exceeds that of the plasma redshift if Ne is greater than 2 · 1012 cm−3.

Also, if some of the electrons have high energy in a magnetic field, the synchrotron absorption(and emission) per cm−3 may exceed that of of the plasma redshift. The photon energy transferred tothe electrons in the plasma redshift is practically independent of the electron energy; but the transferof that energy from the electrons to other particles in the plasma is much slower if the electron energyis high. The hot electrons have then a tendency to become very hot until the synchrotron energylost equals the plasma redshift energy gained. In this case the intensity of the synchrotron energyfrom the thermal and the fast electrons can become much higher than the thermal energy emissionfrom the plasma.

The good astrophysicists of the past did not know about plasma redshift. They could not explaintherefore the very low thermal emission of the coronal plasma around the BHC or SMBHC; but theyaccepted it as a fact in the conventional ”advection dominated accretion flow” (ADAF) model [15,16, 17, 18, 19, 20]. They also could not understand the high emission intensity in the low frequencylimit at about 1012 Hz. But helped by the observation of significant polarization, they interpretedit correctly as due to synchrotron emission from fast electrons in a magnetic field. They reallydid not understand how the electrons could gain the high energy needed, but they argued that ithad to be produced one way or another, for example, by eruption or flare like processes, which ispartially correct. But as mentioned above, they are also often produced by the plasma redshift,which transfers the plasma redshift energy directly to the electrons. The electrons have thereforeusually a significantly higher temperature than the protons. The electrons diffuse outwards aheadof the protons and accelerate them outwards, confer the solar wind, as shown in section 5.3 of [1].Also the magnetic field accelerates the charged particles outwards. Especially the high energy end ofthese electrons has a difficulty in transferring that energy to other particles and transfers it insteadto synchrotron radiation emission. In SMBHCs this synchrotron radiation is especially large and ismainly responsible for the low-frequency intensity-spectrum around 1012 Hz. In the future, we maybe able to spatially separate this emission and confirm that the synchrotron radiation comes mainlyfrom the outer layers of the SMBHC.

A significant part of the X rays are produced in flares. As shown in section 5.5 of [1], the flaresare initiated by the plasma redshift deep in the atmosphere where the magnetic field is particularlystrong so that the plasma redshift cut-off, given by Eq. (2), moves down into much higher densities.The heating in the flares is caused partially by the plasma redshift and partially by the destructionof the magnetic field. This destruction of the magnetic field is initiated by the plasma redshift.The reconnection of the magnetic field lines is a consequence of this destruction of the magneticfield. The reconnection is a consequence of the magnetic field destruction and not the cause as oftenclaimed.

Beyond the limb of the corona, the atmosphere becomes transparent. Therefore below thefrequency of about ν ≈ 1012 Hz, which is close to maximum intensity, the intensity drops steeply.

Thus, the plasma redshift agrees to a large extent with the model devised by, among others, [15 -20]. The plasma redshift helps explain the assumptions made in devising these models, in particularthe low thermal emissivity, the high intensity synchrotron radiation, and the variable x-ray intensity.


5 The Primordial Matter at the Center of SMBHCs

The photon bubble forms at the center of the BHCs and the SMBHCs, because the outward di-rected exchange forces between the fermions together with the photon pressure dominate the inwarddirected gravitational forces on the fermions and the outer layers of the BHCs and the SMBHCs.The weightless photons are therefore squeezed inward towards the center. We should also realizethat when a matter falls onto the surface of the SMBHCs the increased pressure transplants throughthe hot primordial plasma towards the surface of the photon bubble, which is just inside the BHlimit given by Eq. (4). This pressure at the surface of the photon bubble corresponds to a kineticenergy, which is equivalent to the rest mass of the fermions; see Eq. (6) above. The binding energyof the quarks in the protons and the neutrons reduces the temperature, but the quarks will still haveenergy about equal to their rest mass, although the temperature may decrease from about 7.3 · 1012

(about 940 MeV) to about 1.5 ·1012 (about 192 MeV). They quark particles will then also transforminto photons. At these high temperatures all heavy nuclei will fission into neutrons and protons andclose to the surface of the photon bubble into quark-gluon plasma. We call this primordial matter,because it is about equivalent to the primordial matter in the big-bang.

Interestingly, the photon bubble at the center transfers momentum across the photon bubblefrom one side to the other. Thereby the photon bubble reduces gradually the angular momentum ofthe BHC or the SMBHC. The angular momentum of the BHCs is not conserved therefore as usuallysurmised.

Another interesting point is that the tremendous amount of energy and inertial mass stored inthe photon bubble, due to quakes or disturbances by passing stars or in-falling matter, can releasein short time tremendous amount of energy such as that in the gamma-ray bursts. Not only maythe photon from the photon bubble be released, but also primordial matter may be pushed outwardsin such disturbances. It is thus no wonder that we have the SMBHCs surrounded by star formingregions, which has been difficult to explain.

Interesting also is that because these SMBHCs are very hot, they in some respects behave like”Bohr’s liquid drop model”. As they grow they may oscillated as falling liquid drop and split orlike the U-235 nucleus fission into to two ”drops” pushed apart by the plasma redshift heating inbetween them. Due to imbalance between the magnetic field and the diamagnetic moments, themagnetic field in the two halves may even occasionally have opposite direction. Also this may helppush the two ”halves” apart.

These two ”halves” may then move out of the galaxies and in to the sparse matter of intergalacticspace. There the outer coronal plasma becomes thinner and partially transparent with maximumplasma redshifts, which then decrease with age, as the coronal plasma diffuses into intergalactic space.As this coronal plasma becomes thinner the redshift will decrease. While this is all speculative, itappears to match to some extent the phenomenological description given by Halton Arp and othersof some quasars, and calls thus for further consideration.

absorption, κpl = 3.326 · 10−25Ne per cm, is much greater than the free-free absorption that issurmised by the big-bang cosmologists.

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxWe have that the pressure is p = N k Tp, where N is the number density of the particles in the

plasma, and Tp is the temperature of the particles in the plasma. We have therefore that

aT 4em = 3 p = 3N k Tp dyne cm−2, (8)

N consists mainly of protons, helium ions, and electrons. We have therefore that

N ≈ Np + NHe + Ne ≈ 1.917Ne cm−3, (9)

From Eqs. (22) and (23), we get that Tem of the blackbody emission spectrum is given by

aT 4em ≈ 5.75 Ne k Tp erg cm−3 (or dyne cm−2). (10)

The importance of these equations is that they show that the emission temperature, Tem, of themicrowave and infrared radiation is much smaller than the particle temperature, Tp, in the plasma.


This explains the good thermal insulation and high temperatures of the hot inner layers of theplasma and the low emission temperature or low luminosity from the surface that is observed atfrequencies of the microwave and infrared radiation.

From Eq. (1), we get that the plasma-redshift absorption is κpl = 3.326 · 10−25Ne per cm. Insparse plasma, this is much greater than the free-free absorption. The plasma-redshift absorptionlimits therefore the emission depth to κ−1

pl = 3.0 · 1024/Ne cm. It usually reduces also the free-freeemission intensity to values well below that given by Eq. (24).

The X-ray emission and spectrum is determined mainly by the particle temperature and densityof the outer layers. In their introduction to [53], Yuan et al. mention that the density of the outerlayers is Ne ≈ 130 cm−3 and Tp ≈ 2 keV = 23.2 · 106 K at about 1” ≈ 0.04 pc from the SMBHC.

When we insert these values into Eq. (24), we get that Tem = 133 K. The emission from eachsquare cm of the surface into 2π angle is I = 2σT 4

em, where σ = 4a/c = 5.67 · 10−5 erg s−1cm−2K−4

is the Stefan-Boltzmann constant for emission to one side of a plane surface. The luminosity L =I · A = 35, 876A erg s−1, where A is the area in cm2 facing the observer. We can equate this withthe observed luminosity, which is L = 1036 erg s−1, and get that A = 2.8 · 1031 cm2. In case thearea A is a circle, its radius would be about 3 · 1015 cm ≈ 0.001 pc.

However, we should realize that the SMBHC is surrounded by extensive plasma; even the entirecentral region of the Galaxy has extensive hot plasma. Much of the emission that we observe is fromthis extended plasma surrounding the SMBHC. The dense plasma closer to the SMBHC has muchsmaller radius than the above mentioned ≈ 0.001 pc.

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx We find then that it predicts well many phenomena which have been difficult

to explain, and in no case is there a contradiction between predictions and experimental results.Most important are the many solar experiments, because the temperature and electron densities inthe solar corona and in the transition zone have been measured thoroughly. It predicts well theobserved solar redshift, and many phenomena, such as the spicules and the solar flares.

It is usually assumed that the big-bang model predicts the concentration of the light elements;see Peebles’ monograph [1]; see also Schramm [2] who states: ”The bottom line remains: primordialnucleosynthesis has joined the Hubble expansion and the microwave background radiation as oneof the three pillars of big-bang cosmology”. However, there are large discrepancies between theobservations and the predictions, as Rollinde et al. [3] have pointed out:

• ”In effect, we are faced with explaining a 6Li plateau at a level of about 1000 times thatexpected from BBN”. Generally, the observed values of the elements deviate significantlyfrom the predicted values; and it has been difficult or not possible to explain these deviations.Thus, the experimental support for BBN is dubious.

Spergel (see section 11.2.3 of [4]) finds that: The ”observations appear to require either a signifi-cant modification of our ideas about big-bang nucleosynthesis or the existence of copious amounts ofnon-baryonic dark matter” and ”all of the proposed modifications of big-bang nucleosynthesis (BBN)appear to violate known observational constraints”. Similar concern is echoed by the authors of theReport of the Dark Energy Task Force [5]. The report states:

• ”Dark energy appears to be the dominant component of the physical Universe, yet there isno persuasive theoretical explanation for its existence or magnitude. The acceleration of theUniverse is, along with dark matter, the observed phenomenon that most directly demonstratesthat our theories of fundamental particles and gravity are either incorrect or incomplete.”

We have previously shown [6-12] that a newly discovered plasma redshift, which follows frombasic laws of physics, explains the cosmological redshift (see sections 1 to 4 and Appendix A, andsubsections 5.8 and 5.9 of [6]), the cosmic microwave background (CMB), and the X-ray background(see sections 5.10 and 5.11 and Appendix C of [6]). We have also shown that the observations ofsurface brightness confirm the predictions of the plasma redshift, while contradicting the predictionsof the big-bang cosmology [12].


We have found no need for expansion, dark energy, or dark matter for explaining the observedphenomena. The needs for expansion, dark energy, and dark matter in big-bang cosmology stemmainly from failure to deduce plasma redshift. This in turn leads to failure to recognize intrinsicredshifts, failure to find adequate heating for the solar corona, galactic corona and intergalacticplasma; and failure to realize that a hot intergalactic plasma results in an average density that isabout 1,000 fold the maximum of the average total density in the big-bang cosmology.

Important for the nucleosynthesis is also the fact that contrary to general assumptions, the pho-tons are weightless in a local system of reference, and gravitationally repelled as seen by an observerin a distant system of reference. This discovery, although independent of plasma redshift, becameclear when predictions of plasma-redshift theory were compared with solar redshift experiments; seesections 5.1 to 5.6 of [6] and the theoretical explanation in [9].

The designs and the interpretations of the well executed experiments that have been used toprove the weight of the photons are incorrect, because the designs and the interpretations ignoredwell established quantum effects [9]. The weightlessness of photons in the local system of referencetogether with the plasma redshift eliminates the need for Einstein’s Λ-coefficient.

In the big-bang cosmology, the ad hoc initial conditions for nucleosynthesis are nonphysical.They are hypothesized to be created just after inflation from what is sometimes called an ”inflaton”.How and why this all came about defies physical explanation.

In plasma-redshift cosmology, the conditions for renewal of primordial matter from burned outstar matter follows from conventional laws of physics in objects that are usually considered blackhole candidates (BHCs). Many consider the existence of ”black holes” as proven fact. Like RameshNarayan [13], we refer to these objects as ”black hole candidates”. The conditions for nucleosynthesisare like the condition for BHCs ubiquitous in the universe.

For the readers unfamiliar with the plasma-redshift cosmology, we recap in section 2 some ofthe main elements of it. In section 3, we discuss: 1)why plasma-redshift cosmology has no blackholes, 2) the particles energy during the collapse, 3) the photon spectrum at centers of BHCs, 4) theformation of primordial matter and the nucleosynthesis, 5) the small non-rotating neutron starsand 6) the non-rotating intermediate size neutron stars, 7) the effects of rotation on the BHCs,8) supernova SN 1987A, 9) the supermassive black hole candidates (SMBHCs), 10) the dense plasmasurrounding the BHCs and SMBHCs, 11) the magnetic fields and the jets from BHCs, and 12) thegamma-ray bursts. In section 4 we summarize the major conclusions.

6 Plasma redshift of photons

Photons energy loss through plasma redshift is in some aspects analogous to the fast charged par-ticles’ energy loss through Cherenkov radiation. In both cases the additional energy loss is due tothe dielectric constant. There are also differences. Most of the fast charged particles’ energy lossthrough Cherenkov radiation is emitted and reaches large distances, while usually only a small frac-tion is absorbed close to the interaction site. In case of photons, the entire plasma-redshift energyis quickly absorbed in the plasma close to the interaction site. This absorbed energy, which consistsof very low energy quanta, results in significant heating of the plasma.

Exceptionally, Stark redshifts in plasma are referred to as plasma redshift. These Stark redshiftsshould not be confused with the ”plasma redshift of photons” that is used in this article and definedin reference [6] and Eq. (1) below. Stark shifts are caused by changes in energy levels of the emittingatoms. In the Sun, the Stark shifts are usually about 2.5 % of the second term in Eq. (1) below. Inthe problems dealt with in this article, these Stark shifts are usually insignificant when comparedwith the plasma redshift of photons defined in [6].

Plasma redshift of photons is also related to double and multiple Compton scattering of pho-tons. Regular Compton scattering consists of one incident photon and one scattered or outgoingphoton; but double and multiple Compton scattering consists of one incident photon and two ormore outgoing photons. When one of these outgoing photons has very small energy, the cross sec-tion becomes large. It approaches infinity when one of the outgoing photons’ frequency approacheszero. Heitler [14] thought that he had solved this so-called infrared problem. He estimated that the


corresponding integrated product of energy and cross section is very small, or approximately 1/137of the regular Compton cross section. This is usually correct in ponderable matter, gasses, and inlaboratory plasmas. But Heitler overlooked the fact that when the incident photon penetrates veryhot and very sparse plasmas, the very soft part of the spectrum of the outgoing photon will interactsimultaneously with great many electrons in the plasma. The product of energy (of the scatteredsoft photon) and the cross section is then magnified and becomes large, or 50 % of the regular Comp-ton cross-section multiplied by the photon energy. We call this energy loss of the incident photons”plasma redshift”, because it occurs only in very hot and sparse plasma. The deduction of thisplasma redshift and the necessary conditions for plasma redshift are given in sections 1 to 4 and inAppendix A of [6]. The results of the calculations are given by Eqs. (18) and (20) and Eq. (28) ofthat source, and are summarized in Eq. (1) and (2) below.

6.1 Predictions of plasma redshift compared with observations

The plasma redshift is proportional to the electron density integrated along the photon track fromthe object to the observer at a distance R from the object. The plasma redshift is given by

ln(1 + z) = 3.326 · 10−25

∫ R

0

F1(a)γ

γ0Ne dx = 3.326 · 10−25

∫ R

0

Ne dx +γi − γ0

ξ ω, (11)

where the cross section, F1(a), as a function of a = 3.65 · 105λ0

√Ne/T , is given in Table 1 of [6],

and Ne is the electron density in cm−3 and x is in cm. γi is the initial quantum mechanical photonwidth including the initial pressure broadening (the photon width refers to the half-width at halfmaximum in the Lorentz distribution for the line intensity). Lorentz distribution is the same asthe Breit-Wigner distribution or Cauchy distribution). In the Sun, the Lorentzian form of the linedominates the Gaussian form of the line beyond about three half-widths. This has been used forexperimental determination of the Lorentzian width of the solar photons. The pressure broadeningin the line forming elements can also be estimated theoretically.

The spontaneous photon width is usually broadened significantly by the pressure, including Starkbroadening, in the line forming elements and results in γi. γ0 = 2e2ω2/(3mec

3) = 6.266 ·10−24 ω2 isthe classical photon width; and ω is the cyclic frequency of the incident photon. For the frequencyrange of main interest, we have that ξ ≈ 0.25.

The second term on the right side of the equation is insignificant when dealing with cosmologicalredshifts. But it is usually significant for the small redshifts in the Sun and most of the stars. Thevariations in the photon width, γi, are due to variations in both the intrinsic photon width (or linestrength) and the pressure broadening of the photon width. These variations in turn account forthe variation of the redshifts of the solar lines, including the variation in the center to limb effectfor the different lines. The variations in the intrinsic photon width and the pressure broadening(including the Stark broadening) of the photon width, γi, is especially important in collapsars, suchas the white dwarfs and BHCs.

In white dwarfs and in BHCs, the pressure broadenings are very large. The second term thenaccounts for most of the observed redshift, which explains the large variations in the redshifts fromone line to another. All these variations have usually been blamed on the turbulent movements in theline forming elements of the photosphere. However, the average line shifts due to these movementsin the solar photosphere are usually close to zero. The Doppler shifts of the lines formed high in thetransition zone to the corona (the spicules region) often do not, however, average out to zero.

In the Sun, the first term on the right side of the plasma-redshift equation, Eq. (1), can bederived from the electron densities, Ne, in and above the transition zone and in the solar corona.The electron densities can be obtained independently, from X-ray measurements and from Comptonscattering measurements. The predicted redshifts match the observed redshifts in the Sun; see, forexample, Fig. (4) in [6].

Just as the plasma redshift explains the solar redshifts, it predicts that all stars, quasars, andgalaxies must have intrinsic redshifts. The intrinsic redshift increases with brightness and size of thestar due to the increase in the electron density integral, the first term in Eq. (1). Of the conventionalstars, the large and hot O stars have the largest coronas and the largest intrinsic redshifts consistent


with observations. Therefore, bright large objects, such as the quasars, have large intrinsic redshifts.Big-bang cosmologists usually deny the existence of these intrinsic redshifts. They also deny thatthe plasmas between objects in a galaxy and in galaxy clusters contribute to the observed redshifts.These denials often lead to misinterpretation of the observations. Such misinterpretations are themain cause of the need for introducing the dark matter.

The denials of quasars’ intrinsic redshifts have lead to the assumption that they were more distantthan their actual distance, and brighter than their actual brightness.

Failure to recognize plasma redshift and the associated Compton effect has also resulted inmisinterpretation of the magnitude-redshift relation for supernova SN Ia. For explaining the observedrelations in accordance with the big-bang cosmology, it was necessary to introduce hypotheticalvariable ”dark energy” and ”dark matter”. The variation in dark energy has also forced big-bangcosmologists to abandon energy conservation, which is fundamental to physics.

Plasma-redshift cosmology explains the magnitude redshift relation for supernovae without anyneed for dark energy or dark matter; nor has it any need for cosmological expansion, because theentire cosmological redshift is caused by plasma redshift. There is therefore no cosmic time dilation[6, 7, and 11]. There are papers that contend to prove the cosmic time dilation. Scrutiny of theseclaims shows that these claims are invalid; see [6, 7, and 11].

The failure to recognize plasma redshift has also lead to misinterpretation of the microwavebackground, and to inability to explain the X-ray background, because the intergalactic space wasassumed cold and empty; see Appendix C of [6].

The failure to recognize the plasma redshift even made it impossible to explain the heating ofthe nearby solar corona.

Starburst galaxies, which are usually brighter than other galaxies, have denser coronas andtherefore large intrinsic redshifts. Due to their relatively large intrinsic redshifts, the big-bangcosmologists surmise that starburst galaxies are relatively distant. They find none or very fewstarburst galaxies nearby. Big-bang cosmologists blame this incorrectly on evolution; see [12].

The angular scatterings of photons in the plasma redshift are practically nil or insignificant. Thisis so because the pertinent energy quanta in the plasma redshift are extremely small and the angularquantum numbers extremely high in the hot sparse plasmas of intergalactic space. However, theconcurrent Raman scatterings on the plasma frequency start to become important at the distancesof the most distant supernovae; see Eq. (52) in [6]. For example, at z = 1.7, the Raman scatteringangle is about 0.08 arcsec, which is consistent with observations. The observed scattering is actuallygreater due to refractions of the photons in inhomogeneous plasma.

The conventional theory of nucleosynthesis and the many phenomena associated with the collap-sars have been difficult to explain. In section 3 below, we will show how plasma-redshift cosmologyhelps explain these phenomena.

6.2 The plasma-redshift cut-off

The plasma redshift is significant only if the plasma densities are very low and the plasma tempera-tures very high. This is the main reason why the plasma redshift was not discovered long time ago.Plasma physicists were usually dealing with relatively dense and cold laboratory plasmas. Plasmaredshift is possible only if the following condition is fulfilled

λ ≤ λ0.5 = 318.5 ·(

1 + 1.3 · 105 B2

Ne

)Te√Ne

A, (12)

where λ is the wavelength of the incident photons in Angstrom units, B is the magnetic field ingauss units, Te is the electron temperature in degrees K, and Ne is the electron density in cm−3.Accordingly, the plasma redshift is not possible in conventional laboratory plasmas or in the reversinglayer and the chromosphere of the Sun, because the densities are too high and the temperatures toolow.

For the shorter wavelengths, λ ≤ λ0.5, of the solar spectrum, the plasma redshift starts low inthe transition zone. For the longer wavelengths, λ ≥ λ0.5, it starts high in the transition zone tothe solar corona. In the middle of the transition zone to a quiescent solar corona the magnetic


field is usually on the order of 5 gauss, the temperature about 500,000 K, and the density aboutNe ≈ 109 cm−3. When we insert these values into Eq. (2), we get that the cut-off wavelength forthe plasma redshift is at λ0.5 ≈ 5, 000 A. This means that photons with wavelengths smaller thanλ0.5 = 5, 000 A will be redshifted more than 50 % of the redshift given by Eq. (1); and those withwavelength larger than λ0.5 = 5, 000 A will be redshifted less than 50% of the redshift given byEq. (1).

In intergalactic space the magnetic field is too small to influence the cut-off given by Eq. (2).But in the Sun it can exceed 1000 gauss deep in the chromosphere. The cut-off zone for the shortestwavelengths may then penetrate deep into the chromosphere and even into the reversing layers. Itmay then initiate eruption and solar flares. The details of how the plasma redshift and the cut-offexplain many solar phenomena that could not be explained before, including the heating of thecorona, the flares, and the spicules is described in section 5.1 to 5.5 of [6].

6.3 The magnitude-redshift and the brightness-redshift relations

In plasma-redshift cosmology, the observed magnitude, m, of a galaxy is a given function of theintrinsic magnitude, M, the Hubble constant, H0, and the redshift, z, without any adjustable pa-rameters. In big-bang cosmology, the magnitude depends, in addition to H0, and z, on nonphysicaltime variable dark energy parameter, ΩΛ, and on a nonphysical dark matter parameter Ωρ.

Although, the plasma-redshift cosmology has no adjustable parameters, it gives equally goodfit to the experimental data along the entire range of z-values; see Eq. (54), Fig. 5, and Fig. (6) of[6], and Fig. (2) of [11]. The good fit of the theoretically expected and the observed magnitude ofSNe Ia along the entire z-range without any adjustable parameters is a strong confirmation of thecorrectness of the plasma-redshift cosmology.

The electron density, Ne = 3.251 · 10−6 H0, is determined from Hubble constant, H0, only, seeEq. (49) of [6]. The observations show that the Hubble constant in intergalactic space is H0 ≈60 km s−1 Mpc−1. The average density in intergalactic space is then Ne ≈ 1.95 · 10−4 cm−3. Theaverage temperature is Te ≈ 2.7 · 106 K.

The above mentioned values for Ne, Te, and H0 are averages per electron (and not per volume).The actual values vary significantly, especially for small distances, because the plasma-redshift heat-ing is a first order process in density, while the X-ray cooling is a second order process in density. Inintergalactic space, this causes formation of huge hot ”bubbles” separated by relatively thin wallsof colder plasma at the surface of the ”bubbles”. This is all consistent with observations.

The surface brightness of galaxies is in plasma-redshift cosmology proportional to 1/(1 + z)3,but in big-bang cosmology it is proportional to 1/(1 + z)4. The experiments show that the sur-face brightness is proportional to 1/(1 + z)3, which confirms the correctness of the plasma-redshiftcosmology [12].

6.4 The plasma-redshift heating

The plasma redshift causes each and every photon to lose a small fraction of its energy when itpenetrates a hot plasma, such as the solar corona. The energy loss of each photon in the plasmaredshift is immediately absorbed by the plasma and causes very significant heating of the plasma.(Plasma redshift should not be confused with the Compton scattering, where only about 1 photon permillion photons suffers Compton scattering on its way through the solar corona, while the remainder999,999 per million do not suffer Compton scattering. Clearly, Compton scattering in the coronacannot explain the solar redshift. The heating by Compton scattering is insignificant.)

The plasma-redshift heating, dq/dx, is equal to the reduction in the photon energy,∫

I(ν) dν,on the distance dx. This is usually the main heating of the quiescent coronas of the Sun, stars,and galaxies, and of the plasmas in interstellar and intergalactic space. Big-bang cosmologists,who did not know about the plasma redshift, could not find a way to heat the coronal, stellar, andintergalactic plasmas. They assumed, therefore, that the intergalactic space was cold and practicallyempty, which conflicted with many observations, including those of the X-ray background.


The high densities in the Galactic corona observed by Pettini et al. [15] require heating notonly by the plasma redshift of Galactic light, but also by the X-rays from intergalactic space. Theplasma from the hot coronas of galaxies spreads throughout the intergalactic space and fills itwith intergalactic plasma. The photons’ plasma redshift in the intergalactic plasma explains thecosmological redshift, the cosmic microwave background (CMB), and the X-ray background; seesubsections 5.8, 5.10 and 5.11 and Appendices A, B, and C of [6].

The observations of the temperatures and the densities of the hot plasmas around some galaxiesindicate that significant fraction of the plasmas must diffuse into intergalactic space, because thekinetic energy of the particles is greater than their potential energy. In big-bang cosmology, it wasdifficult to reconcile this fact with the assumption that the intergalactic space was cold and empty.

The plasma-redshift heating is a first order process in the density, while the cooling processesare second or higher order processes. This causes a ”bubble” structure with very hot bubblessurrounded by colder plasma between the bubbles. The heat conduction from the hot to the coldplaces counteracts extreme temperature differences. These bubble structures, which the big-bangcosmologists could not explain, are seen in intergalactic space [16], within galaxies, and in coronas ofstars [6]. When the cooling dominates, we may see condensation clouds leak (due to gravitation) intothe galaxies. This influx partially compensates diffusion and the galaxy outbursts sending plasmainto intergalactic space. The pressure, which is proportional to T ·N, in intergalactic space is moreconstant than the temperatures and the densities separately. Due to the gravitational potential, thepressure is higher close to the galaxies and the stars, which therefore have intrinsic redshifts. Inbig-bang cosmology, all these redshifts, even in quasars, are interpreted as Doppler shifts.

6.5 The cosmic microwave background

The cosmic microwave background (CMB) is emitted by the intergalactic plasma. According toEq. (1), the plasma-redshift absorption is κpl = 3.326 · 10−25 (Ne)av = 6.486 · 10−29 (H0/60) cm−1.The absorption coefficient is independent of incident photon’s frequency. From the observationsof the supernovae Ia, we obtain Ne = 1.95 · 10−4 cm−3. This corresponds to one Hubble lengthLH = c/H0 = 1/κpl = 1.542 · 1028 cm ≈ 5, 000 Mpc.

An absorption corresponds to an emission. The emission corresponding to the plasma-redshiftabsorption turns out to be the cosmic microwave background. The plasma-redshift absorptionis more than million times greater than the conventionally used free-free absorption at the CMBfrequencies; see Appendix C of [6]. The dominance of the plasma-redshift absorption explains thebeautiful blackbody spectrum of the CMB.

Within the blackbody cavity with a radius of LH = 1/κpl ≈ 5, 000 Mpc, the correspondingblackbody radiation has a temperature obtained by equating in this case the radiation pressure withthe plasma pressure. We have (for details; see section 5.10 and Appendix C of [6])

aT 4CMB = 3NkT, or TCMB =

(3NkT

a

)1/4

= 2.73 K, (13)

where a = 7.566 ·10−15 dyne cm−2 K−4 is the Stefan-Boltzmann constant and k = 1.38 ·10−16 is theBoltzmann constant. TCMB is the temperature of the CMB radiation. The value of TCMB = 2.73 K,shown on the right side, is for N = Np + NHe++ + Ne = 1.917Ne and Ne = 1.95 · 10−4 cm−3, andT = 2.7 · 106 K. The value of Ne is obtained from the cosmological redshift of supernovae. Thegood fit along the entire redshift range between the predicted and the observed magnitude-redshiftrelation [6, 11] for supernovae supports the contention that the density is correct, because otherwisethe Compton scattering would cause the fits to deviate [6, 11]. The particle temperature T canprincipally be obtained independently from the X-ray background.

The CMB has a well-defined blackbody spectrum, because plasma-redshift absorption is about106 to 1014 times greater than the free-free absorption that is usually used. The plasma-redshiftabsorption entirely determines the emission spectrum; see section C1.4 of Appendix C in [6].

The plasma around the galaxies and galaxy clusters have higher plasma densities and the prod-uct of NeT ≈ NeTe is higher due to the gravitational attraction. The peak of the CMB spectrum


therefore shifts slightly towards higher temperatures in direction of clusters such as the great at-tractor. This shift in the peak of the CMB is seen especially in the direction of the Galactic centerplane. This perturbation from distant galaxies and galaxy clusters is rather small, because of thelarge Hubble length, LH = 1/κpl ≈ 5, 000 Mpc, and limited angular resolution.

The CMB is plasma redshifted and Compton scattered like any other radiation. Equal amountis emitted as is absorbed. Interestingly, the plasma-redshift cut-off starts in the range of 105 ≤ ν ≤3·108. Confirming the plasma redshift, the intensities in this frequency range are observed to increasewith decreasing frequency well beyond the intensities of the blackbody spectrum of the CMB. Thisis still another independent confirmation of the plasma-redshift theory and Eqs. (1) and(2). Theconventional big-bang cosmology cannot explain this intensity increase at these low frequencies.

The isotropy of the CMB derives from the fact that

• The radius of the blackbody cavity for generation of the CMB is equal to one plasma-redshiftlength, which is equal to one Hubble length or about 5,000 Mpc and thus very large. TheCompton-scattering length is 50% of the plasma-redshift length.

• There are forces that cause the universe to be uniform on a large scale. When matter con-centrates in one place, we have renewal processes that reverse this trend and push matteroutwards, as we will see in section 3. (In plasma-redshift cosmology, the matter does notdisappear into the BHCs at the centers of the galaxies, as in the big-bang cosmology.)

6.6 Weightlessness of photons

Most important for the explanation of the renewal of matter and many phenomena associated withBHCs is the fact that the photons are weightless in a local system of reference (where the observerand the photons are), but repelled in a reference system of distant observer, such as an observeron Earth looking at photon experiments in the Sun or close to a BHC. This gravitational repulsionof photons cancels the gravitational redshift, when the photons emitted in the Sun are observed onEarth. This most remarkable discovery (because it contradicts general opinion) was made when thepredicted plasma redshift, based on the known electron densities and photon widths in the solarcorona, was compared with measured solar redshifts; see sections 5.6.1, 5.6.2 and 5.6.3, and Fig. (4)in reference [6].

The weightlessness of photons is theoretically unrelated to the plasma redshift. But only whencomparing the observed solar redshifts with the theoretical predictions of the plasma redshift becameit clear that the solar redshift, when observed on Earth, was not caused by Einstein’s gravitationalredshift. The details of the theoretical explanation of the gravitational redshift are given in [9]. Inreference [9], we analyze also the many experiments that were incorrectly interpreted to show thatphotons had weight. This fundamental discovery has great consequences for cosmology. It eliminatesthe need for Einstein’s Λ, it facilitates the explanation of the renewal of matter, and it modifies, butdoes not destroy, the theory of general relativity, as we will see.

In special theory of relativity, Einstein showed that E = mic2, where E is the energy, mi the

inertial mass, and c the velocity of light. In the classical GTR, Einstein made the assumptionthat inertial mass is equivalent to the gravitational mass. This is usually correct, but with a veryimportant exemption. The equivalence does not apply to photons. Einstein made it very clear thatthe equivalence of photons gravitational mass and inertial mass is an assumption or a conjecture.

When expanding the special theory of relativity to the general theory of relativity, Einstein foundit reasonable to assume that the all frequencies of atoms and photons in the Sun are gravitationallyredshifted in the Sun. Einstein assumed further that the photons’ frequencies are constant as photonstravel in the gravitational field to Earth. (In the literature it is often stated that the photons loseenergy or that the photon’s frequency decreases, as the photons move upwards in the gravitationalfield. This is a common misunderstanding. It is not the way Einstein phrased it, or understood it.)

In Einstein’s classical theory, he found it reasonable to assume that the frequency is constantwhen the light waves move from the Sun to the Earth, because as he argued, equally many wavesshould arrive on Earth as leave the Sun. But in quantum mechanics, where light consists of photons,this is an impermissible assumption when the photon length lph is short compared to the distance


traveled. The photon length is lph = 2πτc, where τ is the lifetime of the emitting state. The photonshave a finite length. The solar photons usually have a length of about 1.5 to 30 m and are thereforevery short compared with the distance to Earth. When the photons travel over distances longcompared with the photon length, their frequencies can change as they move in the gravitationalfield. Unfortunately, Pound et al. and many others (see the discussion in [9]) disregarded quantumeffects. They did not take into account that in all cases the height difference of 22.5 m in theirlaboratory experiments was much too small, when the photons they were using had a photon lengthof about 270 m. We have that δE · δt h, where δE is the potential difference of the photons atthe two heights only 22.5 m apart, and δt is the travel time for the photons. Due to Heisenberg’suncertainty principle, the photons had no chance of changing their frequency.

In fact all the many well executed, but incorrectly designed and incorrectly interpreted exper-iments were insensitive to the weight or weightlessness of photons. This includes the space exper-iments that used much too low frequencies and photon lengths often in excess of 10 astronomicalunits (AU).

Only the solar redshift experiments are valid [9]. The solar redshift experiments can only beevaluated properly based on plasma-redshift theory. The solar redshift experiments then showclearly that the photons gravitational redshift is reversed when photons move from the Sun to theEarth. Importantly, the plasma redshift explains the variations from line to line in both the centerredshifts and in the center-to-limb effects. These variations from line to line are due to variationsin the second term, which depends on the photon width γi on the right side of Eq. (1). This secondterm varies with the strength of the line and the pressure broadenings. The often sited redshifts seenin white dwarfs, such as Sirius B, are due to pressure (including Stark) broadening and the plasmaredshifts. They are not due to the gravitational redshifts, as commonly surmised. The redshiftsvary therefore from line to line in these stars.

Some physicists are inclined to consider gravitational repulsion of photons as a conjecture orsome new physics, because it contradicts what is generally surmised to be a fact. However, it isnot a new physics, but a correction of faulty, and quantum mechanically impermissible theoreticalassumptions; and a correction of faulty interpretation of pertinent experiments; see [9] for details.The frequencies of photons behave like frequencies of atoms. When the atoms and the photons movefrom the Sun to the Earth, their gravitationally redshifted frequencies in the Sun are blue shiftedto cancel their gravitational redshift. In case of atoms, we must perform work to lift them up toEarth. In case of photons, the gravitational repulsion of photons does the work, as seen by a distantobserver.

The reversal of photons gravitational redshift does not reverse the luminosity reduction caused bygravitational time dilation. This time dilation (not to be confused with cosmic time dilation in thebig-bang cosmology) corresponds to the slower rates of clocks. The time between the emissions of theindividual photons from the gravitating body is longer. For the photon energy hνbb do and the totalemitted light energy Lbb do measured by a distant observer on Earth, we have due to gravitationalredshift and gravitational time dilation in big-bang cosmology that

hνbb do =hνbb co

(1 + zgr)and Lbb do =

Lbb co

(1 + zgr)2, (14)

where hνbb co is the photon energy and Lbb co is the total luminosity measured by an observer closeto star; and zgr is the gravitational redshift expected according to the conventional theory. In thelast equation, one factor (1 + zgr) is for the reduction in the photon frequency and the other factoris due to the increased time between the emissions of the photons.

The corresponding equations in plasma-redshift cosmology are:

hνbb do = hνbb co and Lbb do =Lbb co

(1 + zgr), (15)

which when compared with Eqs. (4) have one factor (1 + zgr) less in the denominator, because theredshifts of the photons are reversed due to the repulsion of photons, as seen by a distant observer.

In the big-bang cosmology, we expect the photons from the outer layers of a neutron star to begravitationally redshifted when they reach an observer on Earth. In plasma-redshift cosmology this


is not the case, because of the photons gravitational repulsion (weightlessness in the local systemof reference). However, the concurrent plasma redshift is of the same order of magnitude as thegravitational redshift; and it can easily be mistaken to be a gravitational redshift. For distinguishingbetween the two theories, we should take into account that the gravitational redshift and the Dopplerredshifts are in the big-bang cosmology about constant independent of the line, while the plasmaredshifts, due to the second term in Eq. (1), vary usually from line to line due to variation in theline strength or the photon width (= half of the width at half of the maximum intensity of theLorentzian curve for the line, which is not to be confused with the Gaussian form of the line).

The weightlessness of photons as seen by a local observer (repulsion as seen by a distant observer)leads to the conclusion that ”black holes” can not be formed. Before we reach the Schwarzschildradius, the matter under the high pressure and temperature transforms into quark-gluon plasma andweightless photons as seen by the local observer; see section 3. The photons collect at the center ofthe BHC, because the repulsive exchange interactions between the fermions exceed the gravitationalattraction, while neither the exchange interactions or the gravitational attraction act on photons inthe local system of reference.

6.7 The conservation of energy

In plasma-redshift cosmology, the energy is conserved at all times. In big-bang cosmology energy isnot conserved. Instead, it may disappear into a black hole, or it may be created out of nothing inform of a variable dark energy.

For illustrating that in a system of a distant observer (on Earth), the repulsion of photons leadsto conservation of energy, let us consider a particle (for example an electron). At large distance froma BHC, its rest energy is Eo = moc

2 = hνo, where c is the velocity of light and νo the frequencyof the corresponding photon. When this particle is placed at a lower gravitational potential in thegravitational field, it transfers its change in gravitational potential energy, δE, to its surroundingsin form of heat. The total rest energy of this particle at the lower gravitational potential is thenm c2

g = ε mo(c/ε)2 = moc2/ε = hνo/ε = hν, where ε = 1 + zg (see Møller’s Eq. (8.73) and Eq. 10.84

in [17]). When the redshifted photon returns from the lower potential to the original position, itsredshifted frequency and energy hν = hνo/ε is reversed (blue shifted) resulting in energy equal tohνo to cancel the gravitational redshift in accordance with the present theory. The BHC (or thestar) pushes the photon outwards. In doing so it returns the energy δE to the photon. This showsthat the energy is conserved in the present plasma-redshift theory.

Energy conservation at all times underscores the beauty of the plasma-redshift cosmology. Therepulsion of photons in a distant system of reference is equivalent to weightlessness in the localsystem of reference. This weightlessness is very important. It eliminates the need for Einstein’s Λ,the need for expansion and the black holes; and it makes possible eternal renewal of matter.

6.8 The universe is flat

Einstein’s field equation for a static model of the universe leads to (see Møller’s Eq. 12.120 in [17]and Einstein [18])

1R2

=4π G

c4

(ρc2 + p

)cm−2, (16)

where R is the curvature radius of the universe; ρc2 is the energy density and p is the scalar pressuredensity. Einstein assumed that the pressure density, p, was insignificant compared to the energydensity, ρc2. According to Einstein, we have then (see Eq. (12.121) of [17], or Eq. (14) of [18]) that

1R2

≈ 4π G

c4ρc2 =

4π G

c2ρ (17)

In the big-bang cosmology the summation of baryonic and dark matter densities as a fraction ofthe critical density is estimated to be about Ωρ = 0.3. For H0 = 72, we get ρ = 3ΩρH

20/(8πG) =

1.88 · 10−29Ωρ h2 = 2.92 · 10−30 g cm−3. The curvature radius in Eq. (7) is then R = 6, 200 Mpc,corresponding to z ≈ 1.5. For Ωρ = 1, we get R = 4, 600 Mpc. No curvature has been detected.


In plasma-redshift cosmology, Eq. (7) is not valid, because the average photon pressure oppositethe gravitational attraction is p ≈ −ρc2 in Eq. (6). Eq. (7) does not take into account the conversionof matter to photons and the gravitational repulsion of photons, which results in outward directedmomentum that is transferred to the particles; see subsection 2.6 above and the references thereinfor details.

In Eq. (6), we therefore insert an average value for p = −ρc2, where ρ is the average density inthe universe. The energy balance requires that the outwards repulsion equals inwards attraction,the way Einstein wanted it to be when he introduced Λ. Eq. (6) then takes the form

1R2

≈ 4π G

c4(ρc2 + p) ≈ 4π G

c4(ρc2 − ρc2) = 0 . (18)

These values of ρ and p are averages over a huge volume with a radius on the order of a Hubblelength. On a much smaller scale these equations are not valid, and the matter and photon densitieswill vary from place to place. Therefore, the curvature is positive some places, and negative otherplaces. From this we can understand why on large scale the universe is flat, while on a small scale,we have small curvatures causing gravitational bending of light around gravitating bodies. Thecurvature of space causes 50 % of the bending and the gravitational variation in speed of light theremaining 50 %. The bending is independent of the frequency and the repulsion of photons.

Einstein pointed out that we could not use Newton’s gravitational laws out to distances ap-proaching infinity, because the gravitational potential then becomes infinite. However, due to therepulsion of photons, the outwards directed pressure from the photons will balance the inwardsdirected gravitational pressure and make the universe gravitationally stable over huge dimensionswithout Einstein’s Λ. This balance of the average outward pressure and the inward pressure, asgiven by Eq. (8), makes the universe flat (that is, without curvature) on a large scale.

Besides Eq. (8), there is a second reason for the universe to be flat. When the field from agravitating object acts on a distant particle, for example, a proton or its subunits, it must transmitboth the strength and the direction of the field to the particle. In classical mechanics any suchaction is instantaneous, but according to the uncertainty principle in quantum mechanics any suchaction takes a finite time. The time it takes to recognize an energy transfer, δE, increases aboutinversely proportional to the involved energy, δE. We have that

δτ ≈ h

δE≈ h

(G m1 m2 δR/R2). (19)

While during δτ a particle is finding out the strength and direction of the gravitational field froma distant object, it will be bombarded many times by the Fourier field of the surrounding particles.This bombardment changes the orientation, the strength, and the angular momentum of the particlebefore it can recognize the strength and the direction of the very weak gravitational field from adistant body. Contrary to Einstein’s beliefs, the universe can therefore be infinite and flat on a largescale.

6.9 Black holes in big-bang cosmology

In the conventional big-bang cosmology, black holes (BHs) must be formed. Neither matter nor pho-tons can escape the black holes. Accordingly, classical black holes cannot emit blackbody radiationand their blackbody temperature must be zero, as seen by a distant observer on Earth. Principally,any phenomenon inside a black hole is beyond the realm of classical physics.

However, Stephen Hawking has conjectured that due to the uncertainty principle in quantummechanics some radiation could be emitted. This Hawking radiation from a black hole with a massM has a blackbody temperature given by

T =hc3

8πGMkB≈ 6.1 · 10−8 M

MK, (20)

where M is the solar mass, kB the Boltzmann constant, G the gravitational constant, h the Diracconstant, and c the velocity of light. This equation shows that the temperature T is very low unless


the mass M is very small. The Hawking radiation has never been experimentally confirmed, nor hasthe existence of a black hole ever been confirmed.

According to Narayan [13], the BHCs are believed to have masses M greater than 3M to 5M.X-ray binaries appear to have BHCs with masses on the order of 5M to 10M; and centers ofgalaxies are believed to have BHCs on the order of 106 to 109.5 times M.

In light of the gravitational repulsion of photons in the plasma-redshift cosmology, it is of interestthat the inflation in the big-bang cosmology suggests ”ad hoc” that a repulsive, high-energy matterwas initially the driving force. Sometimes, this matter is referred to as a ”repulsive-gravity material”.

7 Nucleosynthesis in plasma-redshift cosmology

This section shows that when the mass of a collapsar increases beyond about 2.2 solar masses,it does not form a black hole, as usually conjectured. At the center, it forms instead a denseweightless photon ”bubble” that prevents the formation of a black hole and facilitates primordiallike nucleosynthesis. The photon ”bubble” is surrounded by a layer of quark-gluon plasma, then aneutron layer, and then a layer of very hot and dense proton-electron plasma.

7.1 No black holes in the plasma-redshift cosmology

In the general theory of relativity (GTR), the gravitational time dilation and the gravitationalredshift are both given by; see Møller’s Eqs. (8.114), (10.62) and (10.65) in [17]

dt =dτ√(√

1− 2 G M/(R c2)− γιuι/c)2

− u2/c2

= ε dτ , (21)

where the proper time τ is the time measured by an observer following the particle; and t is the timemeasured by a distant observer far away from the gravitating body. ε = (1 + zgr) is the GTR factorreplacing the Lorentz factor (1− u2/c2)−1/2 in special theory of relativity (STR). We have that

ε = (1 + zgr) =λgr

λ0(22)

where zgr is the expanded gravitational redshift in big-bang cosmology, which besides the usualgravitational redshift includes the modification by the particles movements, as given by Eq. (11).

When the reference system is not rotating, γι = 0, Eq. (11) takes the form

dt =dτ√

1− 2 G M/(R c2)− u2/c2(23)

where G = 6.673 · 10−8 cm g−1 s−2 is Newton’s gravitational constant, M is the mass inside R, andu the velocity of the particle at the position of R from the center of the BHC.

For u ≈ 0, this equation is valid for 2GM/(Rc2) < 1. We have then that

R > RS ≈2 G M

c2= 1.485 · 10−28 M = 2.95 · 105 M

Mcm . (24)

where RS , the Schwarzschild radius or the radius of the black hole in the big-bang cosmology. Itmarks the radius where even light cannot escape. When R approaches this limit, the time increment,dt, approaches infinity, and the frequency of light and the temperature approach zero. Close to theRS-limit, we get when we multiply Eq. (14) by mc2/RS that

mc2 ≈ 2 G M m

RS, or mc2 − G M m

RS≈ G M m

RS= Ekin = Qheat , (25)

where mc2 = m0c2 +Ekin is the total energy; m0c

2 is the rest energy; and Ekin is the kinetic energyof the particle. If the particle is stopped, the kinetic energy is transformed into Qheat. We see that


mc2 is twice the loss in potential energy, G M m/RS , which is equal to the kinetic energy gained ina free fall. mc2 = 2Ekin, therefore, Ekin is equal to the rest energy of the particle. This assumesthat the particle’s energy loss as it falls towards this limit is negligible. The fusion energy (evenfusion resulting in iron) is an insignificant (less than 1%) part of rest energy.

In Eqs. (11) and (13), we may have that the value of u2/c2 approaches 2GM/R′sc

2. The corre-sponding singularity is then at the Schwarzschild radius of

R′s ≈

2 G M

c2+

2 G M

c2=

4 G M

c2= 2RS . (26)

From Eq. (13), we see that any thermal motion, u, causes the Schwarzschild radius R′s to increase

beyond RS . The term with γι in Eq. (11) in a rotating system (Kerr black hole), cannot eliminate theincrease in Schwarzschild radius with u . Also electrical and magnetic fields affect the Schwarzschildradius. Due to the thermal motions and the fields, the radius R′

s has a distribution.Close to Schwarzschild radius of the BHC, a local observer with a local clock measuring the

time differential dτ sees the environment differently from that of a distant observer on Earth, whomeasures the corresponding time differential dt. To the local observer at R that is only slightlylarger than RS , the time dτ may be short, the frequency normal, and the temperature very high;but a distant observer sees in all cases dt approach infinity and the frequency and the temperatureapproach zero. This is true in both the big-bang and the plasma-redshift cosmologies.

The gravitational field affects not only time as in Eq. (11), but it affects also the mass, the velocityof light, and the spatial dimensions. All the equations are in plasma-redshift cosmology the sameas the conventional equations. The difference is only in the way the photon frequency varies whenthe photon moves from the gravitating body (such as the Sun) outwards to a distant observer (forexample on the Earth). In plasma-redshift cosmology, the photon frequency increases and cancelsthe gravitational redshift as the photon moves outwards (see section 2.6 above), while accordingto Einstein’s GTR the photon’s gravitationally redshifted frequency stays constant as the photonsmove outwards, for example, from the Sun to the Earth.

The plasma-redshift cosmology accepts the conventional assumptions of physics, which demandthat the time t in Eq. (11) is real at all times. In plasma-redshift cosmology, we cannot, therefore,have a black hole. In the following we show how the plasma-redshift cosmology can easily deny theexistence of a black hole. In contrast, the big-bang cosmology always results in black holes.

7.2 A particle’s energy as it approaches the BH limit

According to Eq. (15), we have that when a particle with mass m at a position R > RS approachesthe RS limit, its kinetic energy, Ekin, approaches the particle’s rest energy, or

Ekin ≈G M m

RS=

m c2

2=

m0 c2 + Ekin

2, or Ekin ≈ m0 c2. (27)

This equation shows that if during the collapse a particle approaches RS , the energy released will beabout equal to the loss in gravitational potential energy, GMm/RS , which is equal to the particlesrest-mass energy, Ekin = m0 c2. When a particle with rest mass m0 moves from infinity to thesurface at R of a BHC, the energy gained is not equivalent to G M m/R, as usually believed, butthe particle’s rest-energy m0 c2 = GMm/RS . This correction of the conventional calculations isimportant, because it significantly increases the heating at the center of the BHC. This rule appliesonly to collapsars with photon bubbles at their centers. The weight of the particle at the surfacewill squeeze the mass of the collapsar to release, mostly close to the center of the BHC, a totalenergy equal to m0 c2. This rough estimate disregards energy losses to the surroundings, becausethe collapse takes a short time, and because the particles fall collectively towards the black holelimit. Any small eruption of matter at the time of impact will fall back on the collapsar.

Eq. (17) is valid for any particle mass m, be it the mass of the proton, neutron, any nuclear unit,or even a chunk of matter. A proton’s kinetic energy close to RS is about equal to its rest-massenergy of 938 MeV. The kinetic energy of the iron nucleus would be about 56 · 938 = 52, 500 MeV.


However, before any large mass unit, such as an iron nucleus, transforms into photon energy, itwill usually fission into hadrons, such as protons and neutrons, which in turn may fission into thefundamental particles, such as the quarks and the antiquarks, the leptons (which include electrons(e), muons (µ), and tau particles (τ , ) and their antiparticles and the corresponding neutrinos),and the bosons (which include photons, gluons, Z-bosons, and W-bosons). The fission and fusionenergies of nuclei amount to a very small fraction of the rest-mass energy, or less than about 0.9 %.

This is consistent with experiments, such as the Relativistic Heavy Ion Collider (RHIC) experi-ments at Brookhaven National Laboratory; see Shuryak [19]. The deconfinement of the quark matteroccurs at temperature on the order of 170 MeV [19, 20, 21], or at about 192 MeV, as some otherestimates indicate [22]. The transformations and heating will absorb most of the energy, which inthe conventional big-bang theory was assumed to disappear into the black hole.

This hot quark-gluon plasma emits weightless photons [23, 24, 25, 26, 27, 28, 29]. The quarksand the leptons are fermions and are therefore governed by the Pauli exclusion principle. Identicalfermions are pushed apart and therefore outwards. The photons, which are bosons, are not governedby the exclusion principle. They will then separate from the fermions and be squeezed inwards andconcentrate at the center of the BHC. The gluons, Z-bosons, and W-bosons usually stay close tothe quarks and the leptons. The weightless photons at the center of the BHC eliminate the blackhole limit or the black hole singularity in Eq. (11), because at the surface of the photon bubble thegravitational attraction is zero.

7.3 The photon spectrum at the center of the BHCs

Just above the surface of the weightless photon bubble, the gravitational attraction on the quark-gluon plasma and neutron layers is close to zero, while the exchange interactions pushing theselayers outwards are large. The photons will then be squeezed towards the center of the collapsar.The pressure in the photon bubble, together with the outward pressure caused by the exchangeinteractions in the quark-gluon plasma and the neutron layers, will counteract the weight of theouter layers.

It is reasonable to assume that Kirchhoff’s law for emission and absorption applies to the photons’interactions with the quark-gluon plasma. This law states that the ratio eλ/aλ between emissioncoefficient and absorption coefficient depends only on the temperature and is independent of thesubstance. The spectrum of photons in the bubble at the center of BHC is likely, therefore, toapproach the blackbody spectrum. This is analogous to the blackbody spectrum of visible lightfrom a blackbody cavity in a solid block in the laboratory.

In the first approximation, the cavity containing the photon bubble (mixed with low density offermions) behaves therefore almost like a blackbody cavity. We have then that the partial pressure,px, of the photons in the bubble surrounded by quark-gluon plasma is given by

px ≈u

3=

4π

3c

∫ ∞

0

Bν(T ) dν =4π

3c

∫ ∞

0

2hν3

c2

1ehν/kT − 1

dν =4σT 4

3c=

aT 4

3≈ ρi c2

3, (28)

where Bν(T ) is the Planck’s function, a = 7.566 · 10−15 erg cm−3 K−4 is the Stefan-Boltzmannconstant, and ρi in g cm−3 is the inertial mass density of photons that is equivalent to the photons’energy density, ρi c2, at the center of BHC.

From the RHIC experiments and the theory for quark-gluon plasma the deconfinement tem-perature for transition to quark-gluon plasma is often estimated to be at about T ≈ Tc = 170MeV [19 - 21]. But the estimates by Cheng et al. [22] indicate that it may be closer to Tc ≈ 192MeV. When we insert these values into Eq. (18), we derive that the inertial mass densities areρi = 1.27 · 1014 g cm−3 and ρi = 2.07 · 1014 g cm−3, respectively; and that the pressures of the pho-tons are px ≈ 3.8 · 1034 dyne cm−2 and px ≈ 6.2 · 1034 dyne cm−2, respectively. The transitions fromthe neutron star to the quark-gluon plasma and to photon bubble at the center is likely therefore tooccur without much contraction.

The temperatures often considered are in the range Tc ≤ T ≤ 2Tc. When the temperatureof the photon bubble is in the range 250 MeV to 350 MeV, the density would be in the rangeρi = 5.98 · 1014 g cm−3, to ρi = 2.29 · 1015 g cm−3. There is practically no limit on how large the


photons’ energy density can be. The photon bubble is therefore elastic, and it would partially bounceback when compressed in the initial collapse. The layers surrounding the bubble, the quark-gluonplasma layer, the neutron layer and the proton-electron layer will dampen the oscillations. All thisappears to be consistent with observations.

The BHCs are thermally insulated by a hot proton-electron plasma surrounding the neutronlayer, as we will see in section 3.10. The temperatures of the different layers are therefore veryhigh. The neutron layer is followed inwards by a layer of quark-gluon plasma, which according toexperiments still behaves more like a liquid than a gas. In BHCs, this layer is followed inwards bya hotter photon bubble at the center, which grows if the BHC accretes mass. Depending on theenvironment, these objects may decrease in mass due to outflow, or they may grow due to accretion;sometimes, to huge supermassive black-hole candidates (SMBHC) at the centers of galaxies.

7.4 Collapsars, primordial matter, and nucleosynthesis

A large, slowly rotating, burned out star will reach a point when the thermal pressure of the particlescan no longer balance the gravitational attraction. The star will then shrink. However, even whenall fusions cease, the exchange interactions between the identical fermions can counter balance thegravitational attraction, but only if the mass, M, of the collapsar is less than 1.4 M, the maximummass for a white dwarf. If M increases beyond this limit, the star collapses further to a neutron starprovided that M is less than about 2.5 M.

In the big-bang cosmology, we have that if the neutron star exceeds M ≈ 2.5 M, the exchangeinteractions between the neutrons cannot prevent a collapse to a black hole. In this case we have that2GM/Rc2 ≥ 1, which according to Eq. (11) and theory of relativity is impermissible. Nevertheless,the big-bang cosmologists usually assume that the black holes are real and do exist, because thephysical laws, as they know them, make it impossible to circumvent their formation. Nothing,not even light, can escape from the black hole. It is usually assumed ”ad hoc”, however, that thegravitational field from the mass falling into the BH escapes and attracts the bodies around the BHin accordance with Newton’s laws of gravitation, as modified by Einstein.

As shown in subsection 3.6, the plasma-redshift cosmology, on the other hand, circumvents theformation of the black hole and the associated contradictions.

According to plasma-redshift cosmology, we have that when a large star collapses, a significantfraction of it will transform into hot quark-gluon plasma that emits photons, or transforms intophotons. The exchange interactions, which involve identical fermions in the quark-gluon plasmalayer and in the neutron layer, push these layers outwards. The emitted photons, which are bosons,collect therefore at the center of the star and prevent thereby the formation of the black hole. Thephotons being bosons can be compressed at will. The photon bubble, which following the initialcollapse is heavily compressed, will therefore bounce back. Some of the energy can result in asupernova eruption, some of it may be released in form of primordial plasma and some in a gamma-ray burst. The collapsar will consist of a hot and dense electron-proton plasma layer surrounding aneutron layer, which surrounds a quark-gluon plasma layer with a photon bubble at the center.

Depending on the environment, any such a BHC may lose mass by emission or an outflow, or itmay grow by accreting mass. Some of the debris from the matter forming the supernova may fallon to the BHC and result in an increase of the photon bubble at the center. The total energy gainedby BHC when a particle falls from infinity onto the surface at R of a BHC is about equivalent to therest mass energy of the particle, which is equal to the change in potential energy when the particlefalls from infinity to the limit RS of a BHC; that is, the energy gained is GM/RS and not GM/Ras usually assumed. This significantly increases the heating at the center of the collapsar.

As we will see in 3.10, the outer layers of a BHC consist of very dense and very hot electron-proton plasma, which is usually so hot that fusion cannot take place. The Compton scatteringin this plasma thermally insulates the BHC. Farther out the temperature will decrease and makepossible some high temperature fusion reactions and the spallation reactions of carbon, nitrogen,and oxygen. These high temperatures and reactions help explain the abundance of isotopes such as6Li, because its formation requires such hot plasma conditions. The concentration of 6Li is about1,000 times higher than that expected in the big-bang cosmology [5]. The thermal emission from the


outermost layer of this plasma is given by Eq. (24) below. This much smaller emission than the oneusually expected, accounts for the observed low luminosity of BHCs and their thermal insulation.The present plasma-redshift cosmology thus gives a natural physical explanation of the much higher6Li content, the much lower luminosity than that expected in the big-bang cosmology, the hightemperatures, the good thermal insulation of the large BHC, and many other phenomena.

A quake caused by rotational stresses, magnetic field stresses, or stresses caused by passage of anearby star may dislocate some parts of the different layers surrounding the photon bubble at thecenter. This may release some of the photons in the bubble together with some quark-gluon plasmaand some of the neutrons. There are many forms of these releases. In sections 3.7 and 3.11, we willdiscuss the important effects of rotations and magnetic fields.

The photons are usually absorbed in the quark-gluon plasma, which then on its way out convertsto neutron, hydrogen, and farther out to light elements such as helium, which may be the principalform exiting through the outer layers. Due to the high temperatures, about 170 - 400 MeV in thephoton bubble and exceeding about 15 MeV in most of the electron-proton plasma layer, usually noheavy atoms would be formed.

Jets may be formed as the protons and electrons accelerate outwards in the divergent magneticfield that is produced by the hot diamagnetic moments in the electron-proton plasma surrounding theBHC, as discussed in section 3.11. These accelerated electrons and protons may create X-rays andcyclotron radiation. In some cases the photons may escape before being absorbed in the quark-gluonplasma. Such a release would be in form of gamma-ray bursts.

These conditions mimic to a large extend the primordial conditions. During a release, the photonswill usually be absorbed by and recreate quark-gluon plasma. This then, as the pressure decreases,recreates hadronic matter, primarily, neutrons and protons, because of the high temperature.

We see thus that primordial matter is created in BHCs, which are often close to the center ofgalaxies. All this is in accordance with conventional laws of physics. There is no need for non-physical assumptions as those postulated ad hoc in the big-bang cosmology. The renewal of mattermay be magnified when the masses of the BHCs increase to that of supermassive black hole candidates(SMBHCs) at the centers of galaxies. The primordial matter in the BHCs leads to nucleosynthesissimilar to that in the conventional theory. However, there are minor differences. The hot, high-density plasmas surrounding the BHCs facilitate nucleosynthesis of such isotopes as 6Li.

7.5 Small non-rotating neutron stars

For a non-rotating neutron star with mass M ≈ 1.4M, we can use the equation of state assumed byAkmal et al. [31], as modified by Olson [30], or by Kratstev and Sammarruca [32]. A neutron star withdensity equal to the normal nuclear energy density, which is about 153 MeV fm−3 or 2.73·1014 g cm−3,would have a partial (along each axis) pressures of about px = 1.27 · 1033 dyne cm−2. The energydensity at the center of a 1.4 M star with radius of about 12.7 km will be about 317 MeV fm−3,corresponding to a mass density at the center of 5.65 · 1014 g cm−3. The corresponding partialpressure at the center would be px = 2.44 · 1034 dyne cm−2; see [30].

According to Eq. (14), we have for v = 0 a black hole radius of RS = 2GM/c2 ≈ 1.4 · 2.95 =4.13 km. A gravitational redshift at R = 12.7 km for u = 0 in Eqs. (11) and (12) would bezgr = ε−1 = (1−2GM/Rc2)−1/2−1 = 0.22, where 2GM/Rc2 = 4.13/12.7 = 0.325. However, abovethe neutron layers, we have less dense electron-proton plasma layers. The radius of the correspondingphotosphere should then exceed 12.7 km with corresponding smaller redshifts. A larger observedredshift indicates therefore that it is a plasma redshift and not a gravitational redshift.

Akmal et al. [31] believe, based on laboratory experiments, that the neutron star becomes unsta-ble when its mass increases and approaches M ≈ 2.2 M. They set an upper limit of M ≈ 2.5 M.Laboratory experiments make it likely that at the centers of such stars, matter transforms to quark-gluon plasma [32]. These predictions are crude but consistent with observations [32, 33, 34, 35].

According to plasma-redshift cosmology, the quark-gluon plasma at the center of the star close tothe upper limit of M ≈ 2.2 M will emit (or transform mass to) weightless photons that concentrateat the center and prevent any part of the star from reaching the black-hole limit. A small bubblehas only a small effect on the conventional equations of state.


From Eq. (14), we can estimate the maximum average density ρs of gravitating mass by equatingMs = ρs (4π/3)R3

S , where RS is the Schwarzschild radius. We get that the average density ρ is

ρ < ρs =Ms

(4π/3) R3S

=3 RS c2

2 G 4π R3S

=3 c2

8π GR2S

=1.6076 · 1027

R2S

= 1.85 · 1016 M2

M2(29)

Thus, the average density of a star with mass M decreases as the mass M increases. For Ms = 1.4M,we get from Eq. (14) that RS = 1.4 · 2.95 · 105 = 4.13 · 105 cm. When we insert this value into theEq. (19), we get that ρs = 9.4 · 1015 g cm−3. This average density required for formation of a blackhole exceeds the center density, 5.65 · 1014 g cm−3, estimated by Olson [30]. The high temperaturesand particle velocities and fields will increase the RS . A neutron star with mass M = 1.4 M, islikely therefore to be stable. Several neutron stars of about this size have been observed.

7.6 Non-rotating, intermediate size neutron stars

When in the conventional big-bang cosmology the inertial mass Mi of a non-rotating collapsar growsbeyond about 2.5 M, it forms a black hole. But in plasma-redshift cosmology, a weightless photonbubble is formed at the center. This bubble is surrounded by quark-gluon plasma and then a neutronlayer surrounded by a hot proton-electron plasma (as explained in subsection 3.10). This thermallyinsulates the collapsar. The RHIC experiments [19] show that the hadrons are not the primaryparticles. When the pressure approaches that at the BH-limit, the mass at the center of the neutronstar transforms into quark-gluon plasma, which in turn emits photons. The outward directed forceson the fermions, which are caused by the exchange interactions between the fermions, cause thephotons to accumulate and form the photon bubble at the center. These weightless photons at thecenter prevent the formation of the black hole.

Example 1. Let us assume that the photon bubble at the center has a radius of about Rph= 5 km.Its weightless inertial mass is then about Mph i = (4π/3) R3

ph ρph i ≈ (4π/3) (5 · 105)3 (5.65 · 1014) =2.96 · 1032 g, or about 0.15 solar masses. We have for this illustration used the center densityρph i = 5.65 · 1014 g cm−3 as a representative value for the inertial mass density of the photonbubble. This is the center density estimated by Olson [30] for a neutron star. Deviations from thisvalue do not affect the main point of this and the following examples used only for illustration ofhow the photon bubble prevents formation of a black hole.

In the plasma-redshift cosmology, the gravitational mass is due to the layers outside the photonbubble, mainly the dense quark-gluon plasma layer and the neutron and electron-proton layers. Thedensity of the quark-gluon plasma and the neutron layer is about ρout ≈ 2.7 · 1014. We will use anaverage density of 3.3 · 1014. If the outer surface of the collapsar is at about R0 ≈ 13.8 km, thegravitational mass Mg ≈ (4π/3)

[(13.8 · 105)3 − (5 · 105)3

](3.3·1014) = 3.4·1033 g, or Mg ≈ 1.7 M.

(We disregard in this and in the following examples the outer layers. This omission does not changethe main point, which is that nature can always prevent the formation of a black hole.)

If this gravitational mass, Mg ≈ 1.7 M, was at the center of the star, the Schwarzschild radiuswould be about 2.95 · 1.7 = 5 km, which is about equal to the photon-bubble radius. Therefore,the black hole couldn’t form. If we included the inertial photon mass of 0.15 solar masses, the totalmass would be about 1.7+0.15 = 1.85 solar masses. The corresponding Schwarzschild radius wouldbe about 2.95 ·1.85 = 5.46 km, and the neutron star would not form a black hole, which is consistentwith the examples in section 3.5.

Example 2. We may have a large photon bubble with a radius of about Rph= 15 km at the center.The inertial mass of the photon bubble is then Mph i ≈ (4π/3) R3

ph ρph i = (4π/3) (1.5 · 106)3 (5.65 ·1014) = 8·1033 g, or about 4 solar masses. In the plasma-redshift cosmology, the gravitational mass isdue to the layers outside the photon bubble, mainly the quark-gluon plasma and the neutron layers.We will use an average density of 3.3 · 1014. If the outer surface of the neutron layer is at aboutR0 ≈ 23.1 km, the gravitational mass Mg ≈ (4π/3)

[(2.2 · 106)3 − (1.5 · 106)3

](3.3·1014) = 1.01·1034

g, or about 5 solar masses. If this mass was at the center, the Schwarzschild radius would be atabout 15 km, which is about equal to the radius of the photon bubble and within the 23.1 km outerradius of the neutron star. The black hole couldn’t form. However, if we included the inertial photon


mass of 4 solar masses in the gravitational mass, the total gravitational mass would be about 4+5= 9 solar masses. The corresponding Schwarzschild radius would be about 2.95 · 9.1 = 26.8 km, andin the big-bang cosmology the neutron star would disappear into a black hole.

These examples, which could easily be expanded to include larger masses, are for illustrationonly. They show how in case of non-rotating stars the plasma-redshift cosmology can always preventthe formation of a black hole; see section 2.6 above. Whenever we approach the black hole limit,the radius of the photon bubble will automatically increase to prevent formation of a BH. Thisapplies also to rotating and non spherical forms of the collapsar, including disk like collapsars andintermediate mass and supermassive black hole candidates (IMBHCs and SMBHCs).

7.7 Effects of rotation on the BHCs

A burned out star usually rotates before it collapses. In the first approximation, the angularmomentum, mr2ω ≈ K0, is conserved during the collapse. The centrifugal force is given bymrω2 = K2

0/(mr3). Therefore, if the radius decreases from a solar radius to a neutron star ra-dius, or by a factor of about 5 ·104, the centrifugal force increases by factor of about (5 ·104)3 ≈ 1014

during the collapse. In case of a small, slowly rotating, burned out star the centrifugal force resultsin an oval shaped collapsar. A larger, fairly fast rotating, burned out star will result in a flattenedcollapsar, with photon layer sandwiched between quark-gluon plasma layers, neutron layers, andouter layers consisting mostly of hot thermally insulating electron-proton plasma.

For a crude overview, we may for M ≤ 2 M, use as a guide the models for ”Fast rotation ofstrange stars” developed by Gourgoulhon et al. [36]. From their estimates and their figures 2 and4, it is clear that the star stretches in the equatorial direction as the rotation increases. When thesurface at the equator exceeds the limit for bound orbit, the star loses mass at the equator.

A collapsar with M ≈ 2M may have a small photon bubble at its center. The binary EXO 0748-676 has been studied by Villarreal and Strohmayer [37], Cottam et al. [38], Wolff et al. [39], andOzel [40]. Villarreal and Strohmayer estimated a slow rotation of ω = 44.7± 0.06Hz. For the samebinary, Cottam et al. estimated a gravitational redshift for three lines, the 2-3 transition in Fe XXVIand Fe XXV ions and 1-2 transition in O VIII, to be zgr = 0.35. When equating the peak flux fromthe X-ray burst with the expected Eddington flux from a M = 1.4M, Wolff et al. estimated adistance to EXO 0748-676 of about 5.9 kpc for a hydrogen dominated burst photosphere, and 7.7kpc for a helium dominated burst photosphere. Using these data, Ozel estimated the mass, radius,and distance to be M = (2.1± 0.28) M, R = 13.8± 1.8 km, D = 9.2± 1.0, see table 2 of [40].

However, the observed redshifts by Cottam et al. [38] are most likely due to plasma redshifts andnot gravitational redshifts; see discussion below Eq. (20). Ozel [40] and Psaltis [41] point out someof the difficulties in determining the redshift. The strong X-ray bursts, which were assumed to be atthe Eddington luminosity limit, are most likely due to release of primordial matter from the core ofthe BHC. The estimates of mass, radius and distance are therefore unreliable. The stiffness observedby Ozel [40] for EXO0748-676 most likely due to the weightless photon bubble at the center.

For determining the mass and the radius for EXO 0748-676, Zhang et al. [42] used three mass-radius relations. They found it impossible to determine the equation of state from the presentlyavailable data. The first example in subsection 3.6 indicates that EXO 0748-676 at its center has asmall photon bubble. This changes the mass-radius relations. It is not surprising therefore that theconventional relations don’t fit the observations.

In the approximation of a non-rotating star, the redshift of z = 0.35 for EXO 0748 676 corre-sponds, according to Eqs. (11) and (12) for a non rotating system, to

1 + zgr = ε =1√

1− 2 G M/(R c2), or

2 G M

R c2=

RS

R= 1− 1

(1 + zgr)2, (30)

For zgr = 0.35, we get RS/R = 0.45. When we insert M = 2.1 M and RS ≈ 2.1 · 2.95 = 6.195 km,

we get R = 13.8 km, which is equal to the radius determined by Ozel. It includes not only theradius of the neutron layer, but also the surrounding plasma layers and the photospheric region. As


pointed out by Ozel [40], the small value of R = 13.8 km for the photospheric radius indicates verystiff equations of state.

The plasma redshifts usually differs from line to line, depending on pressure broadening. A fewlines may, nevertheless, have similar redshifts. This also explains why it has been so difficult to findcoherent redshifts in the spectra of neutron stars in spite of many efforts.

It is thus seen that, when using conventional cosmology, it is very difficult or not possible to ex-plain the observed phenomena in the well-studied EXO 0748-676. On the other hand the phenomenaare easily explained when using the present plasma-redshift cosmology.

In the plasma-redshift cosmology the collapse of a larger rotating star deviates significantlyfrom that expected in the conventional big-bang cosmology.

We saw in subsection 3.6 that a collapse of a large, non-rotating, or slowly rotating, burned outstar leads to a large weightless photon bubble at the center. This prevents the formation of a blackhole. When the star rotates slowly, the maximum stress is often close to the rotational axes. Alongthe rotational axis, this stress may result in release of jets or bursts consisting of very hot primordialmaterial. As we will see in subsection 3.11, jets are especially likely to form in case of strong anddivergent magnetic fields, such as the magnetic dipole fields.

In faster rotating collapsar, the centrifugal forces may flatten the photon bubble so much that it issandwiched between layers of quark-gluon plasma and neutrons, which are surrounded by electron-proton plasma. Most of the photon bubble may be thrown into a torus close to the peripheryof the disk. The thickness of the electron-proton plasma surrounding the collapsar is great manyCompton lengths, and all the inner layers are so hot that fusion can not take place. The primordiallike electron-proton plasma surrounding the collapsar reflects by means of the Compton processemission from the inner layers. These layers are followed by less dense and colder layers, which arefollowed by emission layer, which has a thickness of 3 · 1024 electrons · cm−2 or one plasma-redshiftlength, which is equal to two Compton lengths. The emission from these outermost layer is givenby Eq. (24) in subsection 3.10. This very low emission from the outer layers thermally insulates theBHC. It also accounts for the difficulties in observing the collapsars.

In a fast rotating collapsar the torus contains most of the photon bubble. The greatest stressesis then along the torus, because of the large inertial mass and small gravitational attraction. Thephotons, when streaming through cracks or holes in the torus, will be strongly absorbed in thequark-gluon plasma, which then converts to neutrons and then to electron-proton plasma. Fromthe torus, we may see a release of primordial matter through openings at the equator plane andsometimes along the ridge of the torus.

7.8 SN 1987 A

It has been difficult to explain the observations of the collapse of Sanduleak −69202, a B3 I star,to form SN 1987A in a Type II core-collapse explosion. Nino Panagia [43], who is one of those thathas studied this subject thoroughly, writes:

• ”The early evolution of SN 1987A has been highly unusual and completely at variance withthe wisest expectations. It brightened much faster than any other known supernova: in aboutone day it jumped from 12th up to 5th magnitude at optical wavelengths, corresponding to anincrease of about a factor of thousand in luminosity. However, equally soon its rise leveled offand took a much slower pace indicating that this supernova would have never reached thosehigh peaks in luminosity as the astronomers were expecting. Similarly, in the ultraviolet, theflux initially was very high, even higher than in the optical. But since the very first observation,made with the International Ultraviolet Explorer (IUE in short) satellite less than fourteenhours after the discovery (Kirshner et al. 1987, Wamsteker et al 1987), the ultraviolet fluxdeclined very quickly, by almost a factor of ten per day for several days. It looked as if it wasgoing to be a quite disappointing event and, for sure, quite peculiar, thus not suited to provideany useful information about ”normal” supernova explosions. But, fortunately, this provednot to be the case and soon it became apparent that SN 1987A has been the most valuableprobe to test our ideas about the explosion of supernovae.”


Collapse of such a large star, M ≈ 20 M, was expected by some to result in a black hole, butwe see no indication of that. The excellent phenomenological descriptions of the collapse and itsaftermath show many phenomena that are at odds with that expected as pointed out by Panagia[43]. We do not have a good physical explanation of the very fast brightening (within one day) andthe fast decay of that ultraviolet flux.

No black hole are formed. Plasma-redshift cosmology suggests that before the limit of blackhole is reached, the matter transforms into weightless photons at the center of the collapsar. Noblack hole can therefore be formed; see subsection 3.6.

A huge pulse of brightness must follow immediately after the collapse. The last 2paragraphs of subsection 3.7 give a physical explanation of the tremendous brightness released onthe first day, as described by Panagia [43]. A star with mass of M ≈ 20 M, will during thecollapse release a large fraction of the gravitational potential energy in form of a thermal energy. Afraction of that energy transforms into photons that form a bubble at the center of the collapsar;see subsection 3.3. Due to the fast rotation, the bubble will be thrown outwards and form a torusclose to the periphery of a flattened disk. The photons may concentrate in one or more swellingsalong the torus. Due to rotational stresses, the enclosure around the torus may burst and releasesome of the high-energy photons. These photons will interact with the quark-gluon plasma and theneutrons on their way out and release hot primordial matter together with the high energy photons.This sudden release of primordial matter and intense high-energy photons will fall-off very fast, asthe pressure in the bubble decreases. The relatively short pulse of high-energy photons interactsfirst with circumstellar matter by producing electron-positron pairs, which then ionize and excitethe circum stellar matter. This produces the light echoes and rings as suggested by Panagia [43].

The low luminosity following the relaxation of the initial brightness. Some of theprimordial matter that gushes out will cover up the collapsar with hot electron-proton plasma. TheCompton scattering in this hot and dense electron-proton plasma reflects the high energy radiationfrom inside the collapsar. When relaxed after the initial pulse, the outer most layers of the plasma willcover up the BHC, and will emit infrared radiation that thermally insulates the BHC; see subsection3.10 and Eq. (24). This equation explains why the luminosity is many orders of magnitude smallerthan that from a corresponding hot excited molecular matter. We see often reference to barium andnickel lines emitted from the collapsar. These lines are from the pre-collapse surroundings and notfrom the proper collapsar, which is covered by primordial matter.

How were the rings formed? Usually, it is assumed that the inner and outer rings are leftover debris from explosions in the blue giant when it was a red giant. The plasma-redshift cosmologysuggests a slight modification of this conventional explanation.

Plasma-redshift cosmology shows that all stars must have a corona. Plasma-redshift transfersinitially the energy loss of photons to the electrons [6], which then ionize the atoms. The sphere ofionization stretch far beyond the conventionally estimated Stromgren radii. (Conventional theoryusually assumes incorrectly that the proton temperature is higher than that of the electrons.) Allstars have plasma spheres analogous to the heliosphere. The radius of the heliopause is on the orderof 2.2 · 1015 cm; see Fig. 5 of Opher et al. [44]. Plasma-redshift heating causes the radius of theplasma sphere around stars to increase with their luminosity. Sanduleak-690 202 had a luminosityof L ≥ 105 L, see Nathan Smith [45]. For interstellar densities and magnetic fields similar tothat in the solar neighborhood, we expect the radius of the star’s plasma sphere to be in excess of√

105 = 316 times that of Sun, or in excess of about 7 ·1017 cm. The radius to the colder and denserlayers outside the plasma sphere is likely to be about 1.3 to 1.6 · 1018 cm, the distance to the outerrings of SN1987, as determined by Panagia [43]. Many other factors affect the estimated radius,such as the direction and intensity of the magnetic field, the density and pressure of the interstellarmatter, and the motion of the star relative to the interstellar medium. This is therefore a crudeestimate. It merely makes the formation of the matter around SN 1987-690 202 reasonable withoutany particular explosions.

Plasma redshifts initiates large flares in the Sun [6]. Similar flares are likely to be initiated,especially in large stars like B3 Ia star Sanduleak 690 202. These flares carry large amount of matterinto the far reaches of the corona, especially, along the center plane of the rotation. This may explainthe inner ring.


Very intense high-energy photon beams will stream out through holes or ruptures in the swellingson the torus at the end of the collapse. The torus is unlikely to be uniform with photon bubblesconcentrating in swellings at one or more places. Due to the centrifugal forces, the torus is likelyto rupture a few places, especially in the equatorial plane, but it may also rupture at one or moreplaces along the ridge of the torus. The fast rotation will spray a beam in a circle. This is suggestedonly as a possible explanation of the ring formation.

The rings may diffuse and cool down and become dust rings, as confirmed by Bouchet et al. [46].Most of the very high-energy photons and high energy particles released in the initial flash were not(and due to lack of proper instrumentation could not be) detected. The low grain temperatures,about 166 K, observed by Bouchet et al. [46] does not conflict with the much higher, about 2 · 106

K, temperature in line forming elements observed by Groningsson et al. [47].We see thus that plasma-redshift cosmology gives a reasonable physical explanations of many of

the phenomena around SN187 A. Many of these phenomena could not be easily explained in thebig-bang cosmology.

7.9 Supermassive black hole candidates

In the conventional big-bang cosmology, it is usually assumed that energy and matter disappearfrom this world into a BH. Every galaxy is believed to contain a supermassive black hole (SMBH)with a mass often in the range of 106 to 109 solar masses. Burned out stars and matter, in ourMilky Way Galaxy should accordingly spiral inwards and gradually disappear into the SMBH at thecenter of our Galaxy. Such a SMBH with a mass of about M = 2 · 106M to 4 · 106M has beenlocated in Sagittarius, Sgr A∗, close to the Galactic center.

The big-bang cosmologists thereby abandon energy conservation. While nothing, not even lightcan escape the black hole, they surmise, ad hoc, that the gravitational fields escape the black holes.

In plasma-redshift cosmology, we refer to the corresponding objects as supermassive black holecandidates (SMBHCs), because we have no proof that BH or SMBH exist.

SgrA∗ has been exceptionally well studied [48 - 56]. It has been possible to measure astrometri-cally the orbital parameters of several stars encircling the SMBHC in SgrA∗; see Ghez et al. [46 - 49].The astrometrical measurements of the stars movements appear to give a beautiful and robust in-dication that the mass of Sgr A∗ is about M ≈ 3.7 · 106M. However, we caution that the observedredshifts will to the big-bang cosmologists, who disregard the plasma redshift, indicate too largevelocity variations in the depth direction. This disregard of the plasma redshift increases the esti-mated mass of the SMBHC. Also, besides the gravitational bending of light, the bending of light inthe plasma surrounding the SMBHC should be taken into account. If these effects are not includedin the estimates, the estimated mass of the SMBHC tends to be too large.

While many phenomena appear to conform to the expectations of the big-bang cosmologists, ithas been particularly difficult to understand the youth of the stars in the immediate surroundingsof the SMBHC. These stars appear to belong to a star forming region and not to old nearly burnedout stars usually expected close to the center of the Galaxy. These large and youthful stars consistof O and B stars. For example, a O8-B0 main sequence star with a mass of about 15 M and an ageless than 10 million years has been observed. This has been difficult to understand. Gehz et al. [47]write in their last sentence of the abstract:

• ”Understanding the apparent youth of stars in the Sgr A∗ cluster, as well as the more distantHe I emission line stars, has now become one of the major outstanding issues in the study ofthe Galactic Center.”

Muno et al. [50] (see the introduction section) find that:

• ”In contrast to the Galactic Bulge, the inner 300 pc of the Galaxy is experiencing ongoing starformation...”

These observations contradict the general view, derived from the big-bang cosmology, that the centerof our Galaxy should be filled with old burned out stars.


The plasma-redshift cosmology gives a reasonable explanation of these observations. As shownin sections 3.6 to 3.7, huge amounts of primordial matter streaming out from large BHCs willresult in youthful stars surrounding it. A collapse of a large fast rotating star will result in aflattened neutron star disk, which at the torus containing the photon bubble will result in expulsionof primordial matter, confer subsection 3.8. The expelled primordial matter results in a loss ofangular momentum. The thermally insulating hot electron proton plasma surrounding the SMBHCkeeps its temperature high. Any matter accreting and falling onto the outer surface of this plasma willcorrespond to about equal matter converting to quark-gluon plasma, which then converts to photonsincreasing the photon bubble at the center. The accreting mass will thus result in correspondingamount of rest mass energy released in form of photons at the center. The photon energy at thecenter will compensate the energy losses by emission of photons and of primordial matter. Inplasma-redshift cosmology, this is all self-regulating.

The release processes of primordial matter and photons will reduce, usually in form of smallbursts, the pressure in the photon bubble. The released primordial matter results in formation ofthe young stars in the region surrounding the SMBHC.

7.10 The dense plasma surrounding the BHCs and SMBHCs

The observed dimness and infrared emission from the SMBHC at the Galactic center has beendifficult to explain. In their section 6 of [49], Ghez et al. state:

• ”The radiative emission emerging from the vicinity of our Galaxy’s supermassive black holehas puzzled modelers for three decades. Its total luminosity is only 1036 erg s−1, or 10−9 ofthe Eddington luminosity for a 3.7 · 106 M black hole, most of which is emitted at radiowavelengths. To account for the low luminosity, current models rely on radiative inefficiencyin either, or some combination of, an accretion flow or an outflow (see, e.g., review by Melia& Falcke 2001). Further complicating the picture, recent observations have revealed X-rayand infrared emission, which both show significant variability at timescales as short as tens ofminutes...”.

Ghez et al. [48] (see their Fig. 3), Yuan et al. [51] (see their Figs. 1 through 6) and Yuan etal. [52] (see their Figs. 1 through 5) have shown how the spectral luminosity varies with the frequency.

It is often assumed that the BHCs and the SMBHCs are relatively cold and surrounded bydifferent layers including heavy atom layers. Any evidence for these assumptions is lacking.

Plasma-redshift cosmology indicates that BHC and SMBHC are very hot; so hot that practicallyno heavier atoms can exist. As we have seen, the temperature of the photon bubble at the centerexceeds about 192 MeV, or 2.2 · 1012 K. The electron-proton plasma surrounding the neutron layeris also very hot. Its thickness is many Compton lengths, where one Compton length is LC =1.5033 · 1024 electrons per cm2. If the density with one electron per proton is about 1010 g cm−3,the Compton length would be only 2.51 · 10−10 cm. The Compton scattering in the electron-protonplasma thermally insulates the hot neutron layers. The main insulation, however, is due to the verylow emission, given by Eq. (24), from the outermost plasma layer. This low emission is many ordersof magnitude smaller than that usually assumed. The depth of this outer most photospheric plasmais about one plasma-redshift length or two Compton lengths, or about 3 · 1024 electrons per cm2,which is much smaller than that based on the free-free absorption and emission.

The inner most layers of the electron-proton plasma are therefore very hot. Any fusion is elimi-nated by high energy fission. This inner plasma consists therefore of protons, electrons and neutrons.The temperature of the outer layers decreases gradually. In these layers just below the photosphere,some fusion can take place with formation of helium and then lighter elements. A disturbance canresult in a release of small or large amount of primordial matter. A release of such high densityprimordial matter can result in star formation, even close to the Galactic center. Interestingly, thehigh temperatures and densities of the these outer layers leads spallation and to formation of 6Liand other elements and isotopes that big-bang scenario had difficulties in explaining.


As shown by Brynjolfsson [6]; see App. C and Eqs. C17 and C18 of that source, we have that

p =u

3=

4π

3 c

∫ ∞

0

2hν3

c2

dν

ehν/kTem−1=

4σ

3 cT 4

em =a

3T 4

em erg cm−3, (31)

where all quantities are in cgs units, p is the pressure of the plasma, and u is the kinetic energydensity in the plasma, c is the velocity of light, and h is the Planck’s constant, Tem is temperatureof the emission spectrum, ν is the frequency of the emitted photons, and a = 4σ/c = 7.566 ·10−15 dyne cm−2 K−4 is the Stefan-Boltzmann constant for the energy density.

We have that the pressure is p = N k Tp, where N is the number density of the particles in theplasma, and Tp is the temperature of the particles in the plasma. We have therefore that

aT 4em = 3 p = 3N k Tp dyne cm−2, (32)

N consists mainly of protons, helium ions, and electrons. We have therefore that

N ≈ Np + NHe + Ne ≈ 1.917Ne cm−3, (33)

From Eqs. (22) and (23), we get that Tem of the blackbody emission spectrum is given by

aT 4em ≈ 5.75 Ne k Tp erg cm−3 (or dyne cm−2). (34)

The importance of this equation is that it shows that the emission temperature, Tem, of this mi-crowave and infrared radiation is much smaller than the particle temperature, Tp, in the plasma.This explains the good thermal insulation and high temperatures of the inner layers of this plasmaand the low emission temperature or low luminosity from the surface that is observed at frequenciesof the microwave and infrared radiation.

From Eq. (1), we get that the plasma-redshift absorption is κpl = 3.326 · 10−25Ne per cm. Thisis much greater than the free-free absorption. The plasma-redshift absorption limits therefore theemission depth to κ−1

pl = 3.0 · 1024/Ne cm. It reduces also the free-free emission intensity to valueswell below that given by Eq. (24).

The X-ray emission and spectrum is determined mainly by the particle temperature and densityof the outer layers. In their introduction to [51], Yuan et al. mention that the density of the outerlayers is Ne ≈ 130 cm−3 and Tp ≈ 2 keV = 23.2 · 106 K at about 1” ≈ 0.04 pc from the SMBHC.

When we insert these values into Eq. (24), we get that Tem = 133 K. The emission from eachsquare cm of the surface into 2π angle is I = 2σT 4

em, where σ = 4a/c = 5.67 · 10−5 erg s−1cm−2K−4

is the Stefan-Boltzmann constant for emission to one side of a plane surface. The luminosity L =I · A = 35, 876A erg s−1, where A is the area in cm2 facing the observer. We can equate this withthe observed luminosity, which is L = 1036 erg s−1, and get that A = 2.8 · 1031 cm2. In case thearea A is a circle, its radius would be about 3 · 1015 cm ≈ 0.001 pc.

However, we should realize that the SMBHC is surrounded by extensive plasma; even the entirecentral region of the Galaxy has extensive hot plasma. Much of the emission that we observe is fromthis extended plasma surrounding the SMBHC. The dense plasma closer to the SMBHC has muchsmaller radius than the above mentioned ≈ 0.001 pc.

For ν ≤ 1012 s−1, the luminosity increases about proportional to ν1.4 (see Fig. 1 in Loeb and Wax-man [54]), rather than ν2, as in a one-temperature spectrum. This is so because the pressure, whichis proportional to Ne Tp, decreases outwards. Tem, given by Eq. (24) decreases therefore outwards.For the outermost layers, the peak of the blackbody spectrum shifts then to lower frequencies. Theoutermost layers contribute therefore more to the luminosity at the lowest frequencies than at thehigher frequencies. The emission area is also larger for the lower emission temperatures. In fact, theentire central region of the Galaxy contributes to the lower frequencies. The observed intensities forν ≤ 1012 s−1, are thus consistent with the present explanation. For ν ≥ 1013 s−1 and for X rays, theluminosity is reduced heavily by the greater absorption and Compton scattering. Flares, similar tothose in solar corona [6] and releases of primordial matter from inside the SMBHC cause brightnessfluctuations similar to those observed.


The observations thus confirm that a neutron-star with a photon bubble at its center is surroundedby layers of electron-proton plasma corona. In the deeper layers, the SMBHC is so hot that no heavyatom layer exists. Instead, the neutron layer, with the photon bubble at its center, is surrounded by acorona of protons and electrons. This dense corona insulates thermally the hot neutron star with thephoton bubble at its center. Further out, this plasma emits the observed radiation with intensities,which according to Eq. (24) are several orders of magnitude lower than that expected by the big-bangcosmologists, who did not know about the plasma-redshift cross section.

7.11 Magnetic fields and plasma jets from BHCs

The diamagnetic moments created by the charged particles encircling magnetic field lines are coupledsuch as to direct them in the same direction. The energy density of the field is about equal to thekinetic energy density of charged particles. When the magnetic field moves with the plasma fromhotter region to a colder region, the energy density of the field usually exceeds the kinetic energydensity of the particles. The plasma-redshift heating reverts then the magnetic field energy to heat,just as it does in the solar atmosphere; see subsection 5.5 and Appendix B of [6]. In and above thephotosphere this energy conversion may cause solar flares like eruptions and hot bubbles.

Plasma-redshift together with the magnetic field creates thus hot bubbles with denser plasma, oreven unionized ”clouds”, on the surface of these hot bubbles. These ”clouds” leak due to gravitationinto the SMBHC, just as high velocity clouds leak into the Galaxy [6]. In the solar corona, we alsohave plasma-redshift heating push matter into arches. The condensed plasma leaks down both endsof these arches back into the Sun. These processes are the main source of accretion onto SMBHCand not diffusion, as usually surmised.

Divergence in the magnetic field accelerates the charged particles outwards. In Appendix B of[6], we show (see Eq.B9 of [6]) that the force, FP , on a charged particle at a point P is given by

FP =n

2m v2

P

RP, (35)

which is independent of the magnetic field strength. The particle’s velocity, v⊥, at right angle tothe field is given by

v2⊥ = v2

P

BP

B, (36)

where the magnetic field B at the point P decreases outwards as

B = BP

(RP

R

)n

, (37)

The force given by Eq. (25) pushes the diamagnetic dipole of the charged particles outwards. Thevalue of v2

P may exceed GM/Rc, where Rc is the distance of the point P from the gravitationalcenter, and M is the gravitational mass inside P . The force FP pushing the diamagnetic momentoutwards may therefore exceed the gravitational attraction. We find it likely that this accountsfor the fast jets often seen being pushed outwards from BHC. These jets are fed mainly by theproton-electron plasma surrounding the neutron-star layers. Plasma-redshift cosmology thus givesa natural physical explanation of the jets seen streaming away from many BHC and SMBHC.

7.12 Gamma-ray bursts

As we have seen, the photon bubbles in large BHCs come in many sizes. Many triggers, such aspassage of a star close the BHCs, can initiate an outburst. When the fragile containment opensup and releases the photons, the photons may not have time to react with the quark-gluon plasma,the neutron layers, or the electron-proton plasma surrounding the BHC. A BHC may then releasesuddenly photons equivalent to a small fraction or a large number of solar masses. Such gamma-raybursts come therefore in many sizes. A quiescent SMBHC at the center of our Galaxy releases theprimordial matter and the photons usually in smaller bursts. Initially, the high energy photons


interact with matter mainly by producing electron-positron pairs. The characteristic 511 keV anni-hilation line observed mainly in the galactic center is a clear indicator of this. The often surmisedpositron decay of isotopes seem inadequate for explaining the large intensities reported by Weiden-spointner et al. [57]. Without the present plasma-redshift cosmology, it is difficult to explain theobservations. This appears to be still another confirmation of plasma-redshift cosmology.

8 Summary and conclusions

The plasma-redshift cross section is not hypothetical, as it is derived theoretically from conventionallaws of physics without any new assumptions. It explains great many cosmological phenomena thatin the conventional big-bang cosmology defied physical explanations.

1. Plasma redshift explains the solar redshift, the cosmological redshift, and why all stars, galaxiesand quasars have intrinsic redshifts, because when a photon penetrates a hot sparse plasma,it is redshifted in accordance with Eq. (1) and (2) ; see the deduction in [6]. Plasma redshiftexplains also the heating of the solar corona, the galactic coronas, and the intergalactic space.The energy the photons lose in the plasma redshift is absorbed in the plasma and transformedinto heat [6].

2. The cosmological redshift is not due to expansion as assumed in the big-bang cosmology, but toplasma redshift of photons in intergalactic plasma with average temperature of 2.7 ·106 K, andelectron density of 2 · 10−4 cm−3. Plasma redshift explains the observed magnitude-redshiftrelation for supernovae Ia without any expansion, dark energy, or dark matter [6, 7, 11, 12].

3. Big-bang cosmology assumes cosmic time dilation. Perusal of the experiments, which werethought to prove cosmic time dilation, shows that the proofs are invalid [6, 7, 11]. Consistentwith all observations, the plasma-redshift theory shows that there is no cosmic time dilation.

4. According to the big-bang cosmology, the cosmic microwave background (CMB) originatedin a plasma at a redshift of about z = 1400 [1]. Contrasting this, plasma-redshift cosmologyexplains that the CMB with its beautiful blackbody spectrum is emitted from the intergalactichot plasma without any expansion; see subsection 5.10 of [6]. The required average densityand average temperature are exactly the same as those required to explain the cosmologicalredshift and the X-ray background; see subsection 5.11 and Appendix C of [6].

5. In big-bang cosmology, we cannot explain the X-ray background, because the intergalacticspace is assumed cold and practically empty. In plasma-redshift cosmology, the observed X-ray background follows from the same densities and temperatures of the intergalactic plasmaas those needed to explain the cosmological redshift and the microwave background radiation;see subsection 5.11 of [6].

6. Scrutiny of solar experiments shows that the redshifts, when observed on Earth, are not dueto the gravitational redshifts, but are due to the plasma redshifts given by Eq. (1) and (2); see[6] and [9].

7. The experiments in laboratories and in space that have been assumed to prove photons gravi-tational redshift did not allow adequate time for the change in photons frequency. Heisenberguncertainty principle shows that the time difference between emission and absorption of thephotons was too small for the given potential difference. The experiments were therefore in-correctly designed and the observations incorrectly interpreted [9]. The plasma redshift showsclearly that the photons redshift is reversed when they move from the Sun to the Earth [6].This reversal of the gravitational redshift means that the photons are weightless in the localsystem of reference, but repelled by the gravitational field in the reference system of a distantobserver; see [9].


8. The weightlessness of photons shows that Einstein’s equivalence principle is wrong [9]. Thegravitational mass, mg = 0, of a photon is not equivalent to its inertial mass, mi = hν/c2. Theenormity of this finding for gravitational theory should be appreciated. Presently, we modifythe equivalence principle to apply always, except to photons (possibly to all elementary bosons).

9. When a mass particle approaches the black hole limit during a collapse of a large star, itskinetic energy approaches its rest mass energy, Ekin = m0 c2. Mass then converts to photonsthat accumulate at the center of the collapsar due to repulsive force on the fermions. Theweightless photons at the center prevent the formation of a black hole; see section 3.

10. Time is described with a real number everywhere and at all times, because there are no blackholes; see subsection 3.1. The problem of ever-increasing time and ever-increasing entropy isresolved when we realize that we are usually observing only one half of the material-photoncycle. We usually focus on the physical changes from creation of matter through its changes(which define the time) towards burned out stars and their transformation in large BHCs,while often disregarding the other half of the time cycle; the creation of photons and theirtransformation to matter in an ever lasting renewal process.

11. Although the universe is quasi-static, infinite and ever lasting there is no Olbers’ paradox. Thereduction of the light intensity in the plasma-redshift absorption resolves this problem; see [6].

12. In the big-bang cosmology, the stars will run out of energy and will have a finite lifetime.Plasma-redshift cosmology by contrast leads to eternal renewal of matter and stars, as we haveseen in the present article. The plasma-redshift cosmology leads to transformation of burnedout matter to photon bubbles at the centers of large collapsars. The hot photon bubbles andthe hot centers of large collapsars lead to renewal or recreation of primordial matter. Thisprimordial matter leads to the nucleosynthesis and to formation of new stars; see section 3.

We have demonstrated that plasma redshift, which is based on fundamental and basic conventionalphysics without any new or additional assumptions, leads by necessity to renewal of matter in BHCand thereby to fundamental changes in our cosmological perspective.

References

[1] Brynjolfsson, A., ”Redshift of photons penetrating a hot plasma”, arXiv:astro-ph/0401420v3 7 Oct 2005

[2] Bohr, N., Phil. Mag., 25 (1913) 10

[3] Bohr, N., Phil. Mag., 26 (1913) 1

[4] Bohr, N., Phil. Mag., 30 (1915) 581

[5] Bethe, H., Ann. d. Phys., 5 (1930) 325

[6] Møller, C., Ann. d. Phys., 14 (1932) 531

[7] Møller, C., ”Zur Theorie des Durchgangs Schneller Electronen durch Materie”, A dissertationat the University of Copenhagen. Bianco Lunos Bogtrykkeri (Press) A/A, (1932)

[8] Fermi, E., Phys. Rev., 56 (1939) 1242

[9] Fermi, E., Phys. Rev., 57 (1940) 485

[10] Bohr, N., Kgl. Danske Videnskab. Selskab Mat.-Fys. Medd., 18, No. 8, (1948)

[11] Bohr, A., Kgl. Danske Videnskab. Selskab Mat.-Fys. Medd., 24, No.19, (1948)


[12] Brynjolfsson, A., ”Some aspects of the interactions of fast charged particles with matter”, Adissertation at the University of Copenhagen; available from the author. (1973)

[13] Heitler, W., ”The Quantum Theory of Radiation”, 3rd ed. (Oxford, Clarendon Press, (1954)

[14] Brynjolfsson, A., ”Weightlessness of photons: A quantum effect”, arXiv:astro-ph/0408312v3 17 Feb 2006

[15] Peebles, P. J. E., Principles of Physical Cosmology, Princeton University Press, ISBN 0-691-01933-9, (1993)

[16] Schramm,D.N., Primordial nucleosynthesis, Colloquium paper. Proc. Natl. Acad. Sci. USA,95 (1998) 42

[17] Rollinde, E., Vangioni, E., Olive, K.A., Population III generated cosmic rays and the productionof 6Li, arXiv:astro-ph/0605633 v1 24May 2006

[18] Spergel, D., Particle Dark Matter. In Unsolved Problems in Astrophysics, Ed. J. N.Bahcall andJ. P.Ostriker, Princeton University Press, Princeton, NJ, ISBN 0-691-01607-0, (1997)

[19] Albrecht, A., Bernstein, G., Cahn,R., Freedman, L. W., Hewitt, J., Hu,W., Huth, J.,Kamionkowski,M., Kolb, E.W., Knox, L., Mather, J. C., Staggs, S., Suntzeff N.B., Report ofthe Dark Energy Task Force (DETF), established by the Astronomy and Astrophysics Advi-sory Committee (AAAC) and High Energy Physics Advisory Panel (HEPAP) as a joint sub-committee to advise the Department of Energy, The National Aeronautics and Space Adminis-tration, and National Science Foundation on future dark energy research, astro-ph/0609591 v1Sept 2006

[20] Brynjolfsson, A., Redshift of photons penetrating a hot plasma, arXiv:astro-ph/0401420v3 7 Oct 2005

[21] Brynjolfsson, A., Plasma Redshift, Time Dilation, and Supernovas Ia, arXiv:astro-ph/0406437v2 20 Jul 2004

[22] Brynjolfsson, A., The type Ia supernovae and the Hubble’s constant, arXiv:astro-ph/0407430v1 20 Jul 2004

[23] Brynjolfsson, A., Weightlessness of photons: A quantum effect, arXiv:astro-ph/0408312v3 17 Feb 2006

[24] Brynjolfsson, A., Hubble constant from lensing in plasma-redshift cosmology and intrinsic red-shift of quasars, arXiv:astro-ph/0411666 v3 2 Dec 2004

[25] Brynjolfsson, A., Magnitude-Redshift Relation for SNe Ia, Time Dilation, and Plasma Redshift,arXiv:astro-ph/0602500 v1 22 Feb 2006

[26] Brynjolfsson, A., Surface brightness in plasma-redshift cosmology, arXiv:astro-ph/0605599v2 31 May 2006

[27] Narayan,R., Black holes in astrophysics, arXiv:astro-ph/0506078 v1 14 Jun 2005. To be pub-lished in New J. Phys. 7 (2005) 199

[28] Heitler,W., The Quantum Theory of Radiation, 3rd ed. Oxford Clarendon Press, 1954

[29] Pettini,M., Stathakis, R., D’Odorico, S., Molaro, P., Vladilo,G., ApJ. 340 (1989) 256

[30] Geller, M. J., Huchra, J. P., Real or virtual large-scale structure? Science, 246 (1989) 897-899.

[31] Møller, C., The Theory of Relativity, 2nd ed., Oxford University Press 1972, Delhi, Bombay,Calcutta, Madras, SBN 19 560539


[32] Einstein,A., Sitzungsberichte der Preussuschen Akad. Wissenschaften, (1917) p. 142

[33] Shuryak, E., What RHIC experiments and theory tell us about properties of quark-gluon plasma?,Nucl. Phys. A750 (2005) 64-83, arXiv:hep-ph/0405066 v1 7 May 2004

[34] Karsch, F., Nucl. Phys.,Lattice Results on QCD Thermodynamics A698 (2002) 199, arXiv:hep-ph/0103314 v1 29 Mar 2001

[35] Jacobs, P., Wang,Xin-Nian, Matter in extremis: ultrarelativistic nuclear collisions at RHICProgress in Particle and Nucl. Phys., 54 (2005) 443, arXiv:hep-ph/0405125 v2 19Aug 2004

[36] Cheng, M., Christ, N. H., Datta, S., van der Heide, J., Jung,C., Karsch, F., Kaczmarek, O.,Laermann, E., Mawhinney, R.D., Miao, C., Petreczky, P., Petrov,K., Schmidt, C.,Umeda, T., The transition temperature in QCD, Phys. Rev. D74 (2006) 054507, arXiv:hep-lat/0608013 v3 13 Sep 2006.

[37] Gale, C., Thermal photons and dileptons, arXiv:hep-ph/0512109 v2 8 Dec 2005

[38] Suryanarayana, S. V., Generalized emission function for photon emission from quark-gluonplasma, Phys. Rev., C 75 (2007) 021902, arXiv:hep-ph/0606056 v1 6 Jun 2006

[39] Cozma,M.D., Fuchs, C., Santini, E., Fassler, A., Dilepton production at HADES: theoreticalpredictions, arXiv:nucl-th/0601059 v3 14 Jun 2006

[40] Karsch, F., Lattice simulations of the thermodynamics of strongly interacting elementary par-ticles and the exploration of new phases of matter in relativistic heavy ion collisions, J. Phys.Conf. Ser. 46 (2006) 122, arXiv:hep-lat/0608003 v1 3 Aug 2006

[41] Singh, S. S., Jha, A.K. Electromagnetic radiation from an equilibrium quark-gluon plasma sys-tem, arXiv:hep-ph/0607328 v1 29 Jul 2006

[42] Reygers, K., for the PHENIX collaboration, Direct-photon production production in Au+Aucollisions at RHIC, arXiv:nucl-ex/0608043 v1 24 Aug 2006

[43] Suryanarayana, S. V., Variational method for photon emission from quark-gluon plasma,arXiv:hep-ph/0609096 v1 11 Sep 2006

[44] Olson, T. S., High density neutron star equation of state from 4U 1636-53 observations,arXiv:astro-ph/0201099 v1 7 Jan 2002. Submitted to Phys Rev. C. Also: Olson, T. S., Maximallyincompressible neutron star matter, in Phys. Rev. C. 63 (2001) 105802, arXiv:astro-ph/0011107v2 7 Dec 2000.

[45] Akmal, A., Pandharipande,V. R., Ravenhall, D. G., The equation of state for nucleon matter andneutron star structure, Phys. Rev. C58 (1998) 1804-1828, arXiv:nucl-ph/9804027 v1 13 Apr 1998

[46] Krastev, P. G., Sammarruca, F., Neutron star properties and the equation of state of neutron-rich matter, Phys.Rev. C74 (2006) 025808, Neutron star properties and the equation of state ofneutron-rich matter, arXiv:nucl-th/0601065 v3 24 Jul 2006.

[47] Klahn, T., Blaschke, D., Sandin, F., Fuchs, Ch.., Faessler, A., Grigorian,H., Ropke, G.,Trumper, J., Modern compact star observations and the quark matter equation of state,arXiv:nucl-th/0609067 v1 25 Sep 2006. To be published in ARAA 44 (2006) xx

[48] Remillard,R.A., McClintock, J. E., X-ray Properties of Black-Hole Binaries, arXiv:hep-ph/0606352 v1 14 Jun 2006. To be published in ARAA 44 (2006) xx

[49] Suleimanov,V., Poutanen, J., Spectra of the spreading layers on the neutron star surface andthe constraints on the neutron star equation of state, arXiv:hep-ph/0601689 v2 17 May 2006

[50] Gourgoulhon, E., Haensl, P, Livine, R., Paluch, E., Bonazzola, S., Marck, J. A., Fast rotation ofstrange stars, A &A, 349 (1999) 851, arXiv:astro-ph/9907225 v1 16 Jul 1999


[51] Villarreal, A.R., Discovery of the neutron star spin frequency in EXO 0748-676, arXiv:astro-ph/0409384 v1 15 Sep 2004

[52] Cottam, J., Paerels, F., Mendez,M., Gravitationally redshifted absorption lines in the X-rayburst spectra of a neutron star, Nature 420 (2002) 51-54 arXiv:astro-ph/0211126 v1 Nov 2002

[53] Wolff, M. T., Becker, P.A., Ray, P. S., Wood,K. S., A strong X-ray burst from the low mass X-raybinary EXO 0748-676, arXiv:astro-ph/0506515 v1 21 Jun 2005

[54] Ozel, F., EXO 0748-676 Rules out soft equations of state for neutron star matter, arXiv:astro-ph/0605106 v1 3 May 2006

[55] Ozel, F., Psatis, D., Spectral lines from rotating neutron stars, Astrophys. J. 582 (2003) L31-Le4arXiv:astro-ph/0209225 v1 12 Sep 2002

[56] Zhang,C. M., Yin, H.X., Kojima, Y., Chang, H.K., Xu,R.X., Li, X. D., Zhang, B., Kizilta, B.,Measuring neutron star mass and radius with three mass-radius relations, Mon. Not. Roy. As-tron. Soc. 374 (2007) 232-236 , arXiv:astro-ph/0611659 v1 21Nov 2006

[57] Panagia,Nino, SN1987A: The unusual explosion of a normal type II supernova, A &A, Pro-ceedings of the International Conference: ”1604-2004 Supernovae as Cosmological Lighthouses”,Padova, Italy, June 16-29,2004, arXiv:astro-ph/0410275 v1 11 Oct 2004

[58] Opher,M., Stone, E. C., Liewer, P. C., Gombosi, T., Global asymmetry of the heliosphere,arXiv:astro-ph/0606324 v1 13 Jun 2006

[59] Smith,Nathan, Discovery of a nearly twin of SN 1987A’s nebula around the luminous bluevariable HD168625: Was Sk-690 202 an LBV?, AIP Proceedings of the 5th IGPP ”The Physicsof the Inner Heliosheath: Voyager Observations, Theory and Future Prospects”, arXiv:astro-ph/0611544 v1 16 Nov 2006

[60] Bouchet, P., Dwek, E., Danziger, J., Arendt, R. G., James, I., De Buizer,M., Park, S.,Suntzeff,N. B., Kirshner, R. P., Challis, P., SN1987A after 18 years: Mid-infrared GEMINIand SPITZER observations of the remnant ApJ. 648 (Oct 10, 2006), arXiv:astro-ph/0601495v3 13 Sep 2006

[61] Groningsson, P., Fransson, C, Lundquist, P., Lundquist, N., Chevalier, R., Leibundgut, B., Spy-romilio, J., Coronal emission from the shocked circumstellar ring of SN 1987A, Accepted forpublication in A&A, arXiv:astro-ph/0603815 v2 22 Jun 2006

[62] Ghez,A. M., Duchene,G., Matthews,K., Hornstein, S.D., Tanner,A., Larkin, J., Morris, M.,Becklin, E. E., Salim, S., Kremenek, T., Thompson, D., Soifer, B.T., Neugebauer,G., McLean, I.,The first measurement of spectral lines in a short-period star bound to the Galaxy’s central blackhole: A paradox of youth, ApJ. 509 (2003) L127, arXiv:astro-ph/0302299 v2 6Mar 2003

[63] Ghez,A. M., Salim, S., Hornstein, S. D., Tanner, A., Lu, J. R., Morris,M., Becklin, E. E.,Duchene, G., Stellar orbits around the Galactic center black hole, ApJ. 620 (2005) 744-757,arXiv:astro-ph/0306130 v2 2Nov 2004

[64] Ghez,A. M., Wright, S.A, Matthews,K., Thompson,D., Le Mignant,D., Tanner, A., Horn-stein, S. D., Morris,M., Becklin, E. E., Soifer, B. T., Variable infrared emission from the super-massive black hole at the center of the Milky Way, ApJ. 601 (2004) L159-L162, arXiv:astro-ph/0309076 v2 27 Jan 2004

[65] Ghez,A. M., Hornstein, S.D., Lu, J., Bouchez,A., Le Mignant, D., van Dam, M.A., Wiz-inowich, P., Matthews, K., Morris, M., Becklin, E. E., Campbell, R. D., Chin, J. C.Y., Hart-man, S.K., Johansson, E.M., Lafon,R. E., Stomski, P. J., Summers, D.M., The first laserguide star adaptive optics observations of the Galactic center: SGRA∗’s infrared colorand the extended red emission in its vicinity, ApJ. 635 (2005) 1087-1094, arXiv:astro-ph/0508664 v1 30 Aug 2005


[66] Muno, M. P., Bower,G.C., Burgasser, A. J., Baganoff, F.K., Morris,M.R., Brandt,W. N.,Isolated, massive supergiants near the Galactic center, ApJ. 638 (2006) 183, arXiv:astro-ph/0509617 v1 4 Sep 2005

[67] Yuan, F., Quataert, E., Narayan,R. Nonthermal electrons in radiatively inefficient accretion flowmodels of Sagittarius A∗, ApJ. 598 (2003) 301 arXiv:astro-ph/0304125 v2 29 Jul 2003

[68] Yuan, F., Quataert, E., Narayan, R. On the nature of the variable infrared emission from SGRA∗

, ApJ. 606 (2004) 894 arXiv:astro-ph/0401429 v1 21 Jan 2004

[69] Nagai, M., Tanaka, K., Kamegai,K., Oka, T., Physical conditions of molecular gas in the Galac-tic center Publ. Astron. Soc. Japan, (2007) 1. arXiv:astro-ph/0701845 v1 30 Jan 2007

[70] Loeb, A., Waxman,E., Properties of the radio-emitting gas around SGRA∗, arXiv:astro-ph/0702043 v1 2 Feb 2007

[71] Weidenspointner,G., Knodlseder, J., Jean, P., Skinner,G.K., vonBallmoos, P., Roques, J.-P.,Vedrenne, G., Milne, P., Teegarden, B. J., Diehl, R., Strong,A., Schanne, S., Cordier, B., andWinkler, Ch., The sky distribution of 511 keV positron annihilation line emission as measuredwith integral/SPI, arXiv:astro-ph/0702621 v1 23 Feb 2007

high density plasma in black hole candidates_aps_aprilmeeting_92008

Documents