Black Holes
Outline
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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 Velocity
The 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 Velocity
The 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 =
M /R
R

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 M / R = speed of light.
Event Horizon
Escape velocity < speed of light
Escape velocity = speed of light
R
R
event horizon
Surface Gravities of Different Types of Stars
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).
Red giants
Mass
0.1-100 M
Main sequence 0.1-100 M
White dwarfs <1.4 M
Neutron stars 1.4-3 M
Black holes >3 M
Radius
Earth’s orbit (1000 R)
0.1-10 R
Higher escape velocity
Earth (0.01 R)
Stronger surface gravity
city (0.00001 R)
small town (0.00001 R)
Escape velocity =
M /R
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.
But black holes do have extremely strong gravity near them
because their mass is concentrated in a very small volume
Force on the rocket:
But black holes do have extremely strong gravity near them
because their mass is concentrated in a very small volume
Force on the rocket:
But black holes do have extremely strong gravity near them
because their mass is concentrated in a very small volume
Force on the rocket:
But black holes do have extremely strong gravity near them
because their mass is concentrated in a very small volume
Force on the rocket:
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.
black holes with
masses equal to:
have sizes of:
2 x 10-26 cm
1 cm
3 km
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.
Effect of Gravity on Space and Time
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.
Effect of Gravity on Space and Time
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 Holes
Because 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 Holes
Anything 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.
Making Black Holes
Black holes can sink to the center of galaxies, where they
merge together to form one supermassive black hole.
Making Black Holes
Black holes can sink to the center of galaxies, where they
merge together to form one supermassive black hole.
Making Black Holes
These black holes have masses of >1,000,000 M
The Milky Way’s Sleeping Monster
There’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
Evaporation of Black Holes
“virtual” particles

-
Pairs of virtual particles and anti-particles can
spontaneously pop into existence.
Evaporation of Black Holes
poof
Normally, they very quickly re-combine and annihilate
each other.
Evaporation of Black Holes
“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.
Evaporation of Black Holes
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!