Black Holes. Outline Escape velocity Definition of a black hole Sizes of black holes Effects on space and time Tidal forces Making black holes Evaporation.

Black Holes

Outline

• Escape velocity• Definition of a black hole• Sizes of black holes• Effects on space and time• Tidal forces• Making black holes• Evaporation of black holes

Escape VelocityThe minimum velocity needed to leave the vicinity of a body without ever being pulled back by the body’s gravity is the escape velocity.

Escape VelocityThe escape velocity from a body depends on its mass and on the distance from its center. It is faster for larger mass and smaller distance (i.e., when the body’s gravity is stronger).

Escape velocity =

R

R€

M /R

Escape Velocity

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

Definition of a Black Hole

If the Earth was compressed to a radius of 1 cm, the escape velocity at its surface would be the speed of light (300,000 km/s).

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

The radius at which the escape velocity equals the speed of light is called the event horizon. This is a point of no return.

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

€

M /R

Event Horizon

Escape velocity = speed of light

R

R

Escape velocity < speed of light

event horizon

Surface Gravities of Different Types of Stars

Red giants 0.1-100 M Earth’s orbit (1000 R)

Among the various types of stars, the radii span a much larger range than the masses. As a result, it is mostly the differences in radii that determine the differences in surface gravities so that the stars with smaller radii tend to have stronger surface gravities (higher escape velocities).

Mass Radius

Main sequence 0.1-100 M 0.1-10 R White dwarfs <1.4 M Earth (0.01 R) Neutron stars 1.4-3 M city (0.00001 R) Black holes >3 M small town (0.00001 R)

Escape velocity =

Higher escape velocityStronger surface gravity

Black Holes Don’t Suck

Black holes obey the law of gravity like all other objects. The 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

For instance, 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 black holes do have extremely strong gravity near them because their mass is concentrated in a very small volume







Same gravity

Same gravity

Different gravity

Black Hole Sizes

The radius of the event horizon is the “size” of a black hole. It depends only on the mass of the black hole.

2 x 10-26 cm 1 cm 3 km

black holes with masses equal to:

have sizes of:

Black holes are very compact. The black holes produced by the deaths of massive stars have masses of 3-20 M, corresponding to radii of 10-60 km.

Einstein’s theory of relativity says that a body’s gravity distorts space and time near it. Orbits can be explained as a consequence of this distortion.

Effect of Gravity on Space and Time

The distortion of space-time near a black hole is large because of its intense gravity. The black hole itself can be thought of as a hole in the space-time continuum.


Gravity distorts not just space, but time as well, causing it to slow down. This effect is particularly large within the intense gravity near a black hole. A clock near the event horizon will appear to tick more slowly than a clock far from it. This is called time dilation.


The frequency of light is the number of waves that pass by per second. Because of time dilation, this frequency becomes lower in the presence of gravity, corresponding to longer wavelengths. Thus, light emitted from the vicinity of a black hole will appear redder to an observer far away. This is gravitational redshift.

Tidal Forces near Black HolesBecause gravity becomes very intense near a black hole, tidal forces are also very strong, stretching any nearby object so much that it will be torn into individual atoms.

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 3-20 M.

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

Making Black Holes

Making Black HolesBlack holes can sink to the center of galaxies, where they merge together to form one supermassive black hole.

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

Making Black Holes

The Milky Way’s Sleeping MonsterThere’s even a 2,000,000 M black hole at the center of the Milky Way. We can measure its mass by the motions of stars which pass close to it.

Evaporation of Black Holes

vacuum


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“virtual” particles

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


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

poof


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“virtual” particles

If a virtual pair appear near the event horizon of a black hole, and one particle enters the black hole while the other one travels away from the black hole, then the first particle carries negative energy into the black hole, reducing its energy, and hence its mass. Because of the escaping particle, it appears as if the black hole is producing particles, or radiation. This is called Hawking radiation.


Because of Hawking radiation, black holes slowly lose mass and eventually evaporate. The rate of this mass loss is slower for more massive black holes. Tiny black holes produced during the Big Bang evaporated quickly, but the more massive black holes produced by supernova explosions require more than 1067 years to fully evaporate!

Black Holes. Outline Escape velocity Definition of a black hole Sizes of black holes Effects on space and time Tidal forces Making black holes Evaporation.

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