black holes & relativity. in this chapter you will discover… einstein’s theory of general...
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Black Holes & RelativityBlack Holes & Relativity
In this chapter you will discover…In this chapter you will discover… Einstein’s theory of general relativityEinstein’s theory of general relativity
space and time are not separate entitiesspace and time are not separate entities
how black holes arisehow black holes arise
surprisingly ‘simple’ theoretical properties of surprisingly ‘simple’ theoretical properties of black holesblack holes
X rays and jets of gas are created near many X rays and jets of gas are created near many black holesblack holes
RelativityRelativity
Einstein’s visionEinstein’s visionTheorized Theorized TimeTime & &
DistanceDistance cannot be cannot be measured absolutelymeasured absolutely
TimeTime & & DistanceDistance only only have meaning when have meaning when measured relative to measured relative to somethingsomething
The “Up” ParadoxThe “Up” Paradox In childhood, we regard “up” as a single direction In childhood, we regard “up” as a single direction
above our head.above our head. When we realize that people in Australia do not When we realize that people in Australia do not
stand upside-down…stand upside-down… we revise our common sensewe revise our common sense ““up” is defined relative to the center of the Earthup” is defined relative to the center of the Earth
What is Relative?What is Relative?
A plane flies WEST from Nairobi to Quito at 1,000 mi/hr.A plane flies WEST from Nairobi to Quito at 1,000 mi/hr.
The Earth rotates EAST at the equator at 1,000 mi/hr.The Earth rotates EAST at the equator at 1,000 mi/hr.
What an observer sees depends on her/his position!What an observer sees depends on her/his position!
What is Relative?What is Relative?
A plane flies WEST from Nairobi to Quito at 1,000 mi/hr.A plane flies WEST from Nairobi to Quito at 1,000 mi/hr.
The Earth rotates EAST at the equator at 1,000 mi/hr.The Earth rotates EAST at the equator at 1,000 mi/hr.
An observer on the Earth’s surface?An observer on the Earth’s surface?
=> Would see the plane fly westward overhead=> Would see the plane fly westward overhead
What is Relative?What is Relative?
A plane flies WEST from Nairobi to Quito at 1,000 mi/hr.A plane flies WEST from Nairobi to Quito at 1,000 mi/hr.
The Earth rotates EAST at the equator at 1,000 mi/hr.The Earth rotates EAST at the equator at 1,000 mi/hr.
An observer far away in space?An observer far away in space?
=> Would see the plane not seem to move at all, and the Earth turn => Would see the plane not seem to move at all, and the Earth turn under it!under it!
Motion & ReferenceMotion & Reference
•Objects moving relative to one other are in different reference frames.•They experience time and measure distance & mass in
different ways
Einstein’s VisionEinstein’s Vision
1905: Special Relativity1905: Special Relativity
Speed of Light is the same for ALL observersSpeed of Light is the same for ALL observers
No matter how fastNo matter how fast they are moving! they are moving!
No matter what direction they are moving!No matter what direction they are moving!
Special Relativity ConsequenceSpecial Relativity Consequence
Length is differentLength is different for moving observers for moving observersStationary observers measure longer lengthsStationary observers measure longer lengthsMoving objects appear to be shorterMoving objects appear to be shorter
Time is differentTime is different for moving observers for moving observersStationary observers measure longer timesStationary observers measure longer timesTime for Moving objects appears to be less Time for Moving objects appears to be less
Energy and Mass are related (Energy and Mass are related (E = mcE = mc22))
A ball in moving train…A ball in moving train…
Seen from INSIDE the train, the ball simply goes UP and DOWN in a certain time
tinside observer
A ball in moving train…A ball in moving train…
Seen from OUTSIDE the train, the ball goes UP and DOWN, but ALSO sideways at the
speed of the train, say in a certain time toutside
observer
A ball in moving train…A ball in moving train…
The faster the train is moving, the faster the ball appears to be going to an outside observer
A ball in moving train…A ball in moving train…
The faster the train is moving, the faster the ball appears to be going to an outside observer, covering a longer distance in that same time
toutside observer
So what??So what??
Replace the Replace the BallBall with a with a Beam of LightBeam of Light
And…And…
Suppose both inside and outside Suppose both inside and outside observers observers assume the speed of light is assume the speed of light is the samethe same
A light beam in moving train…A light beam in moving train…
For the observer in the train, the light moves up and down at the speed of light, in a time
tinside observer
A light beam in moving train…A light beam in moving train…
For the observer OUTSIDE the train, the light travels farther ….
A light beam in moving train…A light beam in moving train…
For the observer OUTSIDE the train, the light travels farther ….
– but if it moves at the same speed of light –
it must take longer! toutside > tinside
Consequences!Consequences!
Time measured by someone moving is different than time measured by someone who isn’t!
toutside observer > tinside observer
Consequences!Consequences!
Time measured by someone moving is different than time measured by someone who isn’t!
toutside observer > tinside observer
The faster you go, the greater the difference in your perception of time vs. for someone not moving!
Proof!Proof!
Decay of Subatomic Particles (Muons) Decay of Subatomic Particles (Muons) (cf. http://www.scivee.tv/node/2415 )
Actual Aircraft Travel (Hafele-Keating exp.) Actual Aircraft Travel (Hafele-Keating exp.) (cf. http://www.youtube.com/watch?v=gdRmCqylsME)
GPS satellites!GPS satellites!(cf. (cf. https://www.youtube.com/watch?v=30KfPtHec4shttps://www.youtube.com/watch?v=30KfPtHec4s
(cf. https://www.youtube.com/watch?v=zQdIjwoi-u4 )
Nuclear CollidersNuclear Colliders
Additional Consequences of Additional Consequences of Special RelativitySpecial Relativity
• Time as measured by stationary observer is longer
• Length as measured by stationary observer is longer
• Mass as measured by stationary observer is more
All compared with measurements made by moving observers…
Additional Consequences of Additional Consequences of Special RelativitySpecial Relativity
• Time is relative! (http://www.scivee.tv/node/3025 )
• Time Dilation (cf. http://www.scivee.tv/node/3007)
• Length as measured by stationary observer is longer
• Mass as measured by stationary observer is more
All compared with measurements made by moving observers…
Traveling Traveling to the to the StarsStars
The Doppler Shift Explained through Relativity
Speed of light is measured to be identical but… observed frequency (wavelength) is not!
Einstein’s VisionEinstein’s Vision
1915: General Relativity1915: General Relativity
Acceleration “upward” is equivalent to Acceleration “upward” is equivalent to gravitation “downward”gravitation “downward”
You can’t tell the differenceYou can’t tell the difference
Matter will bend space and timeMatter will bend space and time
Time is affected by gravityTime is affected by gravity
Light is affected by gravityLight is affected by gravityAccording to Einstein’s Theory of According to Einstein’s Theory of
Relativity, Relativity, gravitygravity is really the warping of is really the warping of spacetime about an object with mass.spacetime about an object with mass.
This means that even light is affected by This means that even light is affected by gravity.gravity.
Proof!Proof!
Deflection of Starlight by the SunDeflection of Starlight by the Sun1919 Total Solar Eclipse1919 Total Solar Eclipse
Precession of Mercury’s orbitPrecession of Mercury’s orbit
Gravitational Redshift of light moving upGravitational Redshift of light moving up
Delay in signals from Spacecraft on MarsDelay in signals from Spacecraft on Mars
Radio Signals from MarsRadio Signals from Mars
Mars Orbiters & Landers send signals to Earth
Signals travel at speed of light across solar system
Radio Signals from MarsRadio Signals from Mars
Signals take longer to reach us than predicted
Signals bent by gravitation of the Sun
So what happens to light near a
VERY massive object?
Black HolesBlack Holes
& General Relativity& General Relativity
Black Holes – Theory!Black Holes – Theory!After a massive star supernova, After a massive star supernova,
if core mass > 3 Mif core mass > 3 M, force of gravity , force of gravity will be too strong for even neutron will be too strong for even neutron degeneracy to stabilize star.degeneracy to stabilize star.
The star will collapse into a The star will collapse into a singularity.singularity.
This is what we call a This is what we call a black holeblack hole..
Black Holes - TheoryBlack Holes - Theory
The star becomes infinitely small.The star becomes infinitely small. it creates a “hole” in the Universeit creates a “hole” in the Universe
Since 3 MSince 3 M or more are compressed into or more are compressed into an infinitely small space, the force of an infinitely small space, the force of gravity gravity NEARNEAR to the star is HUGE!!! to the star is HUGE!!!
WARNING!!WARNING!!Newton’s Law of Gravity is no longer valid !!Newton’s Law of Gravity is no longer valid !!
Black Holes - TheoryBlack Holes - Theory
Defined by their Defined by their event horizonevent horizonRadius inside of which light cannot Radius inside of which light cannot
escape (Schwarzschild radius)escape (Schwarzschild radius)
Black Holes - TheoryBlack Holes - Theory
Defined by their Defined by their rotationrotationRapidly rotating holes will affect space Rapidly rotating holes will affect space
around them around them
Rotating Black Holes “drag” space around them
Black Holes - TheoryBlack Holes - Theory
Defined by their Defined by their event horizonevent horizonRadius inside of which light cannot Radius inside of which light cannot
escape (Schwarzschild radius)escape (Schwarzschild radius)Defined by their Defined by their rotationrotation
Rapidly rotating holes will affect space Rapidly rotating holes will affect space around them around them
But how can they be observed??But how can they be observed??
Black Holes affect Time in nearby space
Black Holes affect matter in nearby space, too
Cygnus X-1•A candidate for a *stellar-sized* black hole
•~ 11x more massive than Sun.
•8000 ly away.
Black Holes can emit “jets” of radiation
Black Holes come in different sizes…
Black Holes at the Centers of Galaxies
Intermediate Mass Holes?
Gamma Ray Bursters
Gamma Ray Bursts as indicators of Black Holes
Detecting the “Gravitational Dance” of
Black Holes?
Summary of Key IdeasSummary of Key Ideas
• If a stellar corpse is more massive than about 3 Msun, gravitational compression overcomes neutron degeneracy (or the theorized quark degeneracy pressure) and forces it to collapse further and become a black hole.• A black hole is an object so dense that the escape velocity from it exceeds the speed of light.
The Relativity Theories
Special relativity reveals that space and time are Special relativity reveals that space and time are intimately connected and change with an intimately connected and change with an observer’s motion.observer’s motion.
As seen by observers moving more slowly, the As seen by observers moving more slowly, the faster an object moves, the slower time passes faster an object moves, the slower time passes for it (time dilation) and the shorter it becomes for it (time dilation) and the shorter it becomes (length contraction).(length contraction).
According to general relativity, mass causes According to general relativity, mass causes space to curve and time to slow down space to curve and time to slow down (gravitational redshift). These effects are (gravitational redshift). These effects are significant only near large masses or compact significant only near large masses or compact objects.objects.
The Relativity Theories
Observations indicate that some binary star systems harbor black holes. In such systems, gases captured by the black hole from the companion star heat up and emit detectable X rays and jets of gas.
Supermassive black holes exist in the centers of many galaxies. Intermediate-mass black holes exist in clusters of stars. Very low mass (primordial) black holes may have formed at the beginning of the universe.
Inside a Black Hole
The event horizon of a black hole is a spherical The event horizon of a black hole is a spherical boundary where the escape velocity equals the speed of boundary where the escape velocity equals the speed of light. No matter or electromagnetic radiation can escape light. No matter or electromagnetic radiation can escape from inside the event horizon. The distance from the from inside the event horizon. The distance from the center of the black hole to the event horizon is called the center of the black hole to the event horizon is called the Schwarzschild radius.Schwarzschild radius.
The matter inside a black hole collapses to a singularity. The matter inside a black hole collapses to a singularity. The singularity for nonrotating matter is a point at the The singularity for nonrotating matter is a point at the center of the black hole. For rotating matter, the center of the black hole. For rotating matter, the singularity is a ring inside the event horizon.singularity is a ring inside the event horizon.
Matter inside a black hole has only three physical Matter inside a black hole has only three physical properties: mass, angular momentum, and electric properties: mass, angular momentum, and electric charge.charge.
Inside a Black Hole Nonrotating black holes are called Schwarzschild black Nonrotating black holes are called Schwarzschild black
holes. Rotating black holes are called Kerr black holes. holes. Rotating black holes are called Kerr black holes. The event horizon of a Kerr black hole is surrounded by an The event horizon of a Kerr black hole is surrounded by an ergoregion in which all matter must constantly move to ergoregion in which all matter must constantly move to avoid being pulled into the black hole.avoid being pulled into the black hole.
Matter that approaches a black hole’s event horizon is Matter that approaches a black hole’s event horizon is stretched and torn by the extreme tidal forces generated stretched and torn by the extreme tidal forces generated by the black hole; light from the matter is redshifted; and by the black hole; light from the matter is redshifted; and time slows down.time slows down.
Black holes can evaporate by the Hawking process, in Black holes can evaporate by the Hawking process, in which virtual particles near the black hole become real. which virtual particles near the black hole become real. These transformations of virtual particles into real ones These transformations of virtual particles into real ones decrease the mass of a black hole until, eventually, it decrease the mass of a black hole until, eventually, it disappears.disappears.
Gamma-Ray Bursts
Gamma-ray bursts are events believed to be Gamma-ray bursts are events believed to be caused by some supernovae and by the caused by some supernovae and by the collisions of dense objects, such as neutron collisions of dense objects, such as neutron stars or black holes. Some occur in the Milky stars or black holes. Some occur in the Milky Way and nearby galaxies, whereas many occur Way and nearby galaxies, whereas many occur billions of light-years away from Earth.billions of light-years away from Earth.
Typical gamma-ray bursts occur for a few tens of Typical gamma-ray bursts occur for a few tens of seconds and emit more energy than the Sun will seconds and emit more energy than the Sun will radiate over its entire 10-billion-year lifetime.radiate over its entire 10-billion-year lifetime.
Key TermsKey Terms
accretion diskblack holecosmic censorshipergoregionevent horizongamma-ray burstgravitational radiationgravitational redshiftgravitational waveHawking processintermediate-mass black holeKerr black holeprimordial black hole
Schwarzschild black holeSchwarzschild radiussingularityspacetimesupermassive black holetheory of generalrelativitytheory of special relativityvirtual particlewormholeWolf-Rayet stars
WHAT DID YOU THINK?
Are black holes empty holes in space? If Are black holes empty holes in space? If not, what are they? not, what are they?
No, black holes contain highly compressed No, black holes contain highly compressed matter—they are not empty.matter—they are not empty.
WHAT DID YOU THINK?
Does a black hole have a solid surface? If not, what is at its surface?
No. The surface of a black hole, called the event horizon, is empty space. No stationary matter exists there.
WHAT DID YOU THINK?
What power or force enables black holes to draw things into them?
The only force that pulls things in is the gravitational attraction of the matter in the black hole.
WHAT DID YOU THINK?
How close to a black hole do you have to be for its special effects to be apparent?
About 100 times the Schwarzschild radius.
WHAT DID YOU THINK?
Can you use black holes to travel to different places in the universe?
No, most astronomers believe that the wormholes predicted by general relativity do not exist.
WHAT DID YOU THINK?
Do black holes last forever? If not, what Do black holes last forever? If not, what happens to them? happens to them?
No, black holes evaporate.No, black holes evaporate.