13.3 Black Holes: Gravity’s Ultimate Victory

• Our Goals for Learning

• What is a black hole?

• What would it be like to visit a black hole?

• Do black holes really exist?

What is a black hole?

A black hole is an object whose gravity is so powerful that not even light can escape it.

Question: Escape Velocity

The surface gravity force of a planet of mass M and radius R on a rocket of mass m is

F = G × M × m ÷ R2

To escape an object’s gravity, a rocket must overcome that force, which the rocket does by reaching escape velocity. If you increase the force, you increase the rocket’s required escape velocity.

So… what happens to the escape velocity from an object if you shrink the object?

What happens to the escape velocity from an object if you shrink the object?

1. Escape velocity decreases, because radius decreases

2. Escape velocity doesn’t change, since the mass is the same

3. Escape velocity increases, because radius decreases

What happens to the escape velocity from an object if you shrink the object?

1. Escape velocity decreases, because radius decreases

2. Escape velocity doesn’t change, since the mass is the same

3. Escape velocity increases, because radius decreases

Escape Velocity

Final KineticEnergy

Initial Gravitational Potential Energy

=

=

(escape velocity)2 G × (planet mass)

2 (planet radius)

Light would not be able to escape Earth’s surface if you could shrink the Earth to a radius < 1 cm

The “surface” of a black hole is the radius at which the escape velocity equals the speed of light.

The “surface” of a black hole is the radius at which the escape velocity equals the speed of light.

This spherical surface is known as the event horizon.

The “surface” of a black hole is the radius at which the escape velocity equals the speed of light.

This spherical surface is known as the event horizon.

The radius of the event horizon is known as the Schwarzschild radius.

A black hole’s mass strongly warps space and time in vicinity of event horizon.

Any mass (not just the mass in a black hole) does to three-dimensional space what a weight does to a two-dimensional rubber surface.

No Escape

Nothing can escape from within the event horizon because nothing can go faster than light.

No escape means there is no more contact with something that falls in. Whatever fell in increases the black hole mass, and can change the spin or charge of the black hole, but otherwise loses its identity (according to General Relativity, but maybe not according to Quantum Mechanics … Hawking’s theory of black hole evaporation).

Neutron Star Limit

• Quantum mechanics says that neutrons in the same place cannot be in the same state

• Neutron degeneracy pressure can no longer support a neutron star against gravity if its mass exceeds about 3 Msun (neutrons with the same state would have to move faster than light to avoid being in the same place at the same time)

• Some massive star supernovae can make a black hole if enough mass falls onto core

Beyond the neutron star limit, no known force can resist the crush of gravity. As far as we know, gravity crushes all the matter into a single point known as a singularity.

Even if we are right, the singularity is inside the event horizon, so it will never be seen by the universe outside.

3 MSun Black Hole

The event horizon of a 3 MSun black hole is also about as big as a small city

Neutron star

Question

Is it easy or difficult to fall into a black hole?

A. EasyB. Difficult

Hint: A black hole with the same mass as the Sun wouldn’t be much bigger than a university campus

How does the radius of the event horizon change when you add mass to a black hole?

Hint: the escape velocity from any black hole is the speed of light

=

(escape velocity)2 G × (object’s mass)

2 (object’s radius)

How does the radius of the event horizon change when you add mass

to a black hole?

1. Decreases

2. Stays the same

3. Increases

How does the radius of the event horizon change when you add mass

to a black hole?

1. Decreases

2. Stays the same

3. Increases

What would it be like to visit a black hole?

If the Sun shrank into a black hole, its gravity would be different only near the event horizon.

If the Sun shrank into a black hole, its gravity would be different only near the event horizon.

The Earth's orbit would not change if the Sun suddenly became a black hole.

If the Sun shrank into a black hole, its gravity would be different only near the event horizon.

The Earth's orbit would not change if the Sun suddenly became a black hole.

Black holes don’t suck!

Light waves take extra energy to climb out of the deep dip in spacetime near a black hole, leading to a gravitational redshift

Time passes more slowly near the event horizon

Tidal forces near the event horizon of a 3 MSun black hole would be lethal to humans

Tidal forces would be gentler near a supermassive black hole because its radius is much bigger

Do black holes really exist?

Black Hole Verification

• Need to measure mass Use orbital properties of companion Measure velocity and distance of orbiting gas

• It’s a black hole if it’s not a star and its mass exceeds the neutron star limit (~3 MSun)

Some X-ray binaries contain compact objects of mass exceeding 5 MSun which must be black holes

One famous X-ray binary with a likely black hole is in the constellation Cygnus

13.4 The Mystery of Gamma-Ray Bursts

• Our Goals for Learning

• What causes gamma ray bursts?

Gamma ray bursts may signal the births of new black holes

Some gamma ray bursts come from extreme supernovae (hypernovae?) in very distant galaxies; others from collisions of 2 neutron stars or a neutron star and a black hole in moderately distant galaxies.

What have we learned?What is a black hole?

• A black hole is a place where gravity has crushed matter into oblivion, creating a true hole in the universe from which nothing can ever escape, not even light.

What have we learned?What would it be like to visit a black hole?

• You could orbit a black hole just like any other object of the same mass. However, you’d see strange effects for an object falling toward the black hole: – Time would seem to run slowly for the object– Its light would be increasingly redshifted as it

approached the black hole.– The object would never quite reach the event

horizon, but it would soon disappear from view as its light became so redshifted that no instrument could detect it.

What have we learned?• Do black holes really exist?• No known force can stop the collapse of a stellar

corpse with a mass above the neutron star limit of about 3 solar masses, and theoretical studies of supernovae suggest that such objects should sometimes form. Observational evidence supports this idea.

What have we learned?

• What causes gamma ray bursts?

• Gamma-ray bursts occur in distant galaxies and are the most powerful bursts of energy we observe anywhere in the universe. No one knows their precise cause, although at least some appear to come from unusually powerful supernovae.

Activity 25, Special Relativity

Part I, page 83

Part IV, page 85-86

MOVING CLOCKS RUN SLOW

MOVING CLOCKS RUN SLOW

• If a clock is moving relative to you, it runs slower than your watch, which is not moving relative to you.

MOVING CLOCKS RUN SLOW

• If a clock is moving relative to you, it runs slower than your watch, which is not moving relative to you.

• From the point of view of someone not moving relative to the clock, you and your watch are moving. So what that person sees is that your watch is running slow relative to their clock.

A CLOCK MOVING RELATIVE TO YOU RUNS SLOWER THAN A CLOCK NOT

MOVING RELATIVE TO YOU

• If a clock is moving relative to you, it runs slower than your watch, which is not moving relative to you.

• TIME IS RELATIVE

• From the point of view of someone not moving relative to the clock, you and your watch are moving. So what that person sees is that your watch is running slow relative to their clock.