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Relativity and Black Holes

Post-MS Evolution of Very High Mass (>15 MΘ) Stars

• similar to high mass except more rapid

• lives end in Type II supernova explosions

• main difference: mass of iron core at end of fusion > 3 MΘ

• core is too massive to form a neutron star!

• must collapse into something even denser – a black hole!

Escape Velocity, ve

Measure of gravitational strength

Minimum speed to escape the gravity of an object

e.g. Earth, ve = 11.2 km/s

ve ↑ mass ↑

ve ↑ size ↓

ve highest for objects which are small and massive i.e. dense!

Neutron Stars, ve = 0.5c

A neutron star only has to become 25% smaller in order to make ve = c

Such an object is so dense that not even light can escape!

Such an object is called a black hole!

Problem: if light has no mass, how can it be affected by gravity?

Newton’s Theory of gravity has no explanation for this!

To understand the properties of black holes we need a new theory of gravity!

Einstein’s Relativity!

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Relative Motion

Since everything in the Universe is in motion, measurements can only be made relatively and not

absolutely!

The Principles of Relativity

1. The Laws of Physics are the same for everyone and are independent of our location or motion in

the Universe

2. The speed of light, c is constant and is the same for everyone and independent of our location or

motion in the Universe

Everything else is relative!

Person Running Towards a Ball Person Traveling Towards Photon

A photon always travels towards an observer at the speed of light, c

regardless of their motion!

Special Theory of Relativity (1905)

Only deals with motion in straight lines and at constant speeds

Is not a theory of gravity!

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Relativistic Effects

Strange things effects are observed when objects are seen traveling close to the speed of light:

• Mass increases!

• Length decreases along the direction of motion! (Lorentz Contraction)

• The rate of passage of time slows down! (Time Dilation)

Lorentz Contraction

Why can’t we travel at or faster than the speed of light?

A object observed to be traveling at the speed of light would be seen to have

• An infinite mass!

• A zero length!

• A rate of passage of time of zero = time stops!

It is impossible to observe these things so it must be impossible to travel at or faster than c!

General Theory of Relativity (1915)

Includes effects of accelerated motion which is the type of motion produced by gravity

Is a theory of gravity!

The Equivalence Principle

The effects of gravity and acceleration are identical

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Conclusion: strong gravitational fields produce the same relativistic effects seen for rapid motion

e.g. time dilation!

Newtonian Gravity: 3 dimension of space + 1 dimension of time

Einstein’s Gravity: 4 dimensions of “space-time”

‘Space-time” is a 4-dimensional surface or hyperspace which is impossible to comprehend

directly but can be thought of as representing the “fabric of the Universe”

A 2D Analogy of 4D Spacetime

Prediction: masses curve the fabric of spacetime around them e.g. a person on a trampoline

Explains:

The action of gravity across distance

The shapes of planetary orbits – they follow the curvature of spacetime around the Sun!

Experimental Confirmation of General Relativity

Gravitational Bending of Light

Light follows the curvature of spacetime around a massive object!

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Precession of the Orbit of Mercury

Mercury’s orbit is not stationary in space due to curvature of spacetime around the Sun

Gravitational Time Dilation

weaker gravity

stronger gravitytime slows

Gravitational Redshift

light loses energy as it escapes from a source of gravity

result: longer wavelengths

Gravitational Waves

Ripples in spacetime caused by the acceleration of masses e.g. core collapse of massive a star

Only prediction of General Relativity not measured

Laser Interferometer Gravitational-Wave Observatory (LIGO) How it works!

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Each interferometer

arm is 4 km long!

Two observatories separated by 2000 miles!

Able to confirm detections!

The Formation of a Black Hole

A Black Hole is Highly Curved Spacetime The Structure of a Black Hole

Schwartzschild Radius, Rsh

Rsh = 3M km

where:

M = mass of black hole is solar masses

Example: a 4 MΘ black hole has a radius of 3 x 4 = 12 km

Common Misconception:

Black holes gobble up all matter for 1000’s of light years around them!

Not so!

Spacetime highly curved close to hole but not far from it!

Example: replace Sun with solar mass black hole –planetary orbits would not change!

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You can only be pulled into a black hole if you are very close to it!

Minimum stable orbit = 3Rsh

Properties of Singularities

• definition: non zero mass occupies zero volume

• a point of infinite density and gravity

• fabric of spacetime breaks – a passage to parallel Universe?

• problem: laws of physics (even relativity) break down!

• have no way of predicting properties!

Problem:

If singularities are places where the laws of physics do not apply, do black holes contradict the

principle of relativity that the laws of physics are the same everywhere?

Law of Cosmic Censorship

Singularities are always surrounded by event horizons

Blocks us from observing the unpredictable properties of singularities

Black holes do not contradict relativity!

Are any properties of black holes measurable?Yes!

But only those properties that can be measured without electromagnetic radiation!

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No Hair Theorem

Only 3 properties can be measured for a black hole:

• mass

• charge

• rotation

Mass

Place a test probe of mass, Mp in orbit around a black hole at a (safe!) chosen distance, a

Measuring the orbital period, P of the probe will allow the mass of the black hole, Mbh to be

determined:

P2 = a3/(Mbh + Mp)

Charge

A charged particle will be attracted or repelled by a black hole if it is charged!

← ● e- →

What is the charge of the hole?

Negative!

Rotation

Frame dragging: close to a rotating black hole spacetime is dragged around

Impossible to be still!

Place probe in ergoregion to

determine rotation!

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Detecting Black Holes

Isolated black holes very difficult to detect!

Easier to detect black holes by the effect they have on neighboring matter e.g. a star

Isolated black holes will distort the light from background objects

Gravitational Microlensing

General Relativity predicts that a black hole should magnify the light from a background star as it passes in front on it due to the distortion of

space-time around it

Cygnus X-1

A very strong X-ray source in Cygnus the Swan

At the location of the X-ray source is a

B0 I star

Is this the source of the X-rays?

A B0 star has T = 25,000 K

Wien’s Law

T = 25,000 K → λmax = UV

The star is not hot enough to produce the X-rays!

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Does the star have a companion?

Spectrum?

Single set of lines from B0 I star

Lines are Doppler shifted back and forth with P = 5.6 days!

A single-lined spectroscopic binary

Conclusion: the companion must be dark and close

Analyze orbit to obtain masses

Mass B0 I star = 30 MΘ

Mass companion = 3-7 MΘ

Properties of Companion

• Emits little visible radiation

• Massive

What could it be?

A black hole!

Where do the X-rays come from?

Cygnus X-1 is a Mass Transfer Binary

The X-rays come from the accretion disk of gas spiralling into the hole

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Still some doubt due to uncertain mass of companion!

If mass companion = 3 MΘ then could be a neutron star!

Better examples of black hole candidates that cannot be neutron stars:

V404 Cygni

Mass companion > 6.26 MΘ

A0620-00 in Monoceros

Mass companion > 3.2 MΘ

IC 10 X-1 in the nearby galaxy IC 10Mass companion 24-33 MΘ

Most massive known stellar mass black hole as of Fall 2007

Thought Experiment

Release a probe and let it fall into a black hole from a safe distance!

Equipment:

• a blue flashing light so you can follow its path

• a video camera to transmit back images

Results?

Video Camera Images

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Gravitational Time Dilation

Initially the probe will accelerate towards the hole

However, as it approaches the event horizon it will appear to slow down due to the strong gravity!

It will only reach the event horizon after an infinite amount of time where it will appear to be frozen in

space!

Gravitational Redshift

As the probe approaches the event horizon the light from the probe is gravitationally redshifted from blue to green to yellow to red and will eventually

become invisible as it shifts into non-visible wavelengths!

It would disappear from view long before it reaches the event horizon!

Tidal Forces

As the probe approaches the hole, tidal forces will distort the shape of the probe!

Eventually the probe will break into pieces!

Wormholes

A shortcut (tunnel) through hyperspace between two distant parts of the Universe allowing very

rapid travel!

Interstellar Travel Through Wormholes

Big problem: we don’t yet know how to create wormholes, and even if we did they would require enormous amounts of energy to form and

keep open!