Black HolesBlack Holes

Outline: Black Holes

• Escape velocity• Definition of a black hole• Event horizon• Gravitational redshift & time dilation• Tidal forces of black holes• Warping of space time• Making black holes

Escape VelocityAccording to Newton, the greater the gravity, the faster an object must go to escape into space. This is called the escape velocity.

Escape Velocity

The escape velocity from any body depends on its mass, and on the starting distance. The escape velocity is larger for larger mass and smaller distance.

Escape velocity =

R

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M /R

Escape Velocity

At the surface of the Earth, the escape velocity is 11 km/s.

Escape Velocity

If Earth is compressed to a radius of 1 cm:

Escape velocity = 300,000 km/s = speed of light

If the Earth is compressed any more, the escape velocity would be greater than the speed of light. So nothing could escape its surface, not even light. This is the definition of a black hole.

The radius at which the escape velocity is greater than the speed of light is called the event horizon.

Anything inside of the event horizon will never return to our universe. This is the point of no return.

Black Hole Sizes

The size (i.e., the radius of the event horizon) of a black hole depends only its mass.

2 x 10-26 cm 1 cm 3 km

Theoretically, anything could become a black hole if it is compressed enough so that = speed of light.

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M /R

Black Holes Don’t Suck

Force of gravity from a black hole is the same as from any other object with the same mass at the same distance.

Black Holes Don’t Suck

The orbit of the Earth would not change if the Sun was replaced with a black hole with the same mass as the Sun.

Force on the rocket:

But they have extremely strong gravity near them because the mass is concentrated in a very small volume

Force on the rocket:

But they have extremely strong gravity near them because the mass is concentrated in a very small volume

Force on the rocket:

But they have extremely strong gravity near them because the mass is concentrated in a very small volume

Force on the rocket:

But they have extremely strong gravity near them because the mass is concentrated in a very small volume

Close to a black hole, gravity is strong. According to relativity: High Gravity Large Acceleration Large Acceleration High Speed High Speed Time Dilation

Time slows down (as you measure it) for someone close to a black hole. This includes atoms – the frequency of emitted light gets smaller. Thus produces a gravitational redshift.

It also means that for an object at the event horizon, time stands still (at least, as you measure it).

Effect of Extreme Gravity on Light

Effect of Extreme Gravity on Light

Even light feels the effect of gravity. Objects with stronger surface gravity bend the path light takes. Black holes bend light so much that it can’t escape and falls back to the black hole.

white dwarf

Another way to look at the relation between black holes and light is to assume that light travels in straight lines, but that mass warps space-time. Orbits (and light) just follow the curve.

Effect of Extreme Gravity on Space-Time

Another way to look at the relation between black holes and light is to assume that light travels in straight lines, but that mass warps space-time. Orbits (and light) just follow the curve.

Effect of Extreme Gravity on Space-Time

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The warping of space-time by the Sun causes light to bend around the Sun.

Effect of Extreme Gravity on Space-Time

Warping of Space-Time

A black hole represents the extreme case where gravity punches a hole in space-time.

Tides near Black HolesGravity depends on mass and distance. Objects such as neutron stars and black holes are very small, yet very massive. So if you get close, the tides may get you!

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Making Black HolesAnything can become a black hole if it is compressed enough.One way that nature makes black holes is through the death of massive stars. These black holes have masses >3 M.

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Black holes can sink to the center of galaxies, where they merge into one supermassive black hole.

Making Black Holes

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Black holes can sink to the center of galaxies, where they merge into one supermassive black hole.

Making Black Holes

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These black holes have masses of >1,000,000 M!

Making Black Holes

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Evaporation of Black Holes

vacuum

Evaporation of Black Holes

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“virtual” particles

Pairs of virtual particles and anti-particles can spontaneously pop into existence. They have positive

and negative energy, so their combined energy is zero.

Evaporation of Black Holes

Normally, they very quickly re-combine and annihilate each other.

poof

Evaporation of Black Holes

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“virtual” particles

If a virtual pair appear near the event horizon of a black hole, and the anti-particle enters the black hole, then

energy (and hence mass) of the black is decreased. If the other particle travels away, then it appears as if the black

hole is producing particles, or radiation.

Evaporation of Black Holes

If a virtual pair appear near the event horizon of a black hole, and the anti-particle enters the black hole, then

energy (and hence mass) of the black is decreased. If the other particle travels away, then it appears as if the black

hole is producing particles, or radiation.

Summary

• Escape velocity• Definition of a black hole: escape velocity is greater

than the speed of light• Event horizon: radius at which the escape velocity =

the speed of light (size of a black hole)• Gravitational redshift & time dilation

– Near a black hole, light is redshifted and clocks slow down

• Tidal forces of black holes• Warping of space time• Making black holes

– Deaths of massive stars make less massive black holes– Mergers of those black holes make supermassive black holes