Transcript Black Holes and Relativity

Black 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 Velocity
According 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 =
M /R
R

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 M / R = speed of light.
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.
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
Force on the rocket:
Effect of Extreme Gravity on Light
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
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
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
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.
QuickTime™ and a
Cinepak decompressor
are needed to see this picture.
Effect of Extreme Gravity on Space-Time
The warping of space-time by the Sun causes light to bend
around the Sun.
Warping of Space-Time
A black hole represents the extreme case where gravity punches
a hole in space-time.
Tides near Black Holes
Gravity 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!
QuickTime™ and a
YUV420 codec decompressor
are needed to see this picture.
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 M.
QuickTime™ and a
Sorenson Video 3 decompressor
are needed to see this picture.
Making Black Holes
Black holes can sink to the center of galaxies, where they
merge into one supermassive black hole.
QuickTime™ and a
YUV420 codec decompressor
are needed to see this picture.
Making Black Holes
Black holes can sink to the center of galaxies, where they
merge into one supermassive black hole.
QuickTime™ and a
YUV420 codec decompressor
are needed to see this picture.
Making Black Holes
These black holes have masses of >1,000,000 M!
QuickTime™ and a
YUV420 codec decompressor
are needed to see this picture.
QuickTime™ and a
Animation decompressor
are needed to see this picture.
Evaporation of Black Holes
vacuum
Evaporation of Black Holes
“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
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 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