Transcript Goal: To get to know the ins and outs of relativity

Goal: To get to know the ins and
outs of relativity (relatively
speaking)
Objectives:
1) To learn about how Black holes depend on
space-time
2) To learn about General Relativity
3) To learn about Special Relativity and why this
is VERY important for the future of interstellar
travel
Black Hole
• What is a black hole?
Black Hole
• A black hole is an object that is either so
massive or so dense that the escape
velocity on its surface is greater than the
speed of light.
• As Einstein discovered nothing can travel
faster than the speed of light.
• Therefore NOTHING, not even light can
escape from a black hole!
No escape!
• The radius at which the escape velocity is
exactly the speed of light is called the
Schwarzschild radius.
• The Schwarzschild radius is an event
horizon.
• An event horizon is a surface where if
something were to pass through it, it is
gone (event horizon = goodbye forever).
But there’s more!
• Mass warps space. Time is relative to
space. Therefore masses warp time also!
• Tobject = Tuniversal / (1 – rs / r)1/2
• Where rs is the Schwarzschild radius (the
radius of the event horizon of a black hole)
• rs = 1.5 km * Mass of object / Mass of our sun
Black hole astrophysics
• What would happen if we swapped our
sun for a black hole of exact equal mass?
• A) The earth would be sucked into the
black hole
• B) Time on the earth would slow down
• C) The earth would be slingshot out of the
solar system
• D) Nothing would happen to the orbit of
the earth or the clocks on earth.
Black hole astrophysics
• What would happen if we swapped our
sun for a black hole of exact equal mass?
• D) Nothing would happen to the orbit of
the earth or the clocks on earth.
• Black holes are not vacuum cleaners.
They obey gravity just like everything else.
• In fact it is harder to run into a black hole
because it is so frikkn small (diameter of 3
km for one the mass of out sun).
Can we “see” black holes?
• Nope, light can’t escape.
• However, we do see them indirectly by watching
stars or accretion disks in orbit around them.
• In fact we find lots of them out there.
• In the center of every galaxy there seems to be
one.
• Ours has a 2.6 million solar mass black hole
(which is small, many galaxies have a black hole
which is over a billion solar masses)
Death of black holes?
• Turns out that black holes can die!
• This is because of Hawking radiation.
• What is this? Well… Long winded answer
coming up that won’t be on the test but is
kinda cool!
Is that all?
• Nope (but that is all for black holes for
now, sorry).
• Special Relativity
• Clocks progress at a rate RELATIVE to
their position in space.
• Velocity slows the progress of an object’s
clock so that:
• Tobject = Tuniverse / gamma
• Gamma = 1 / (1 – v2/c2)1/2
Interstellar travel
• Tobject = Tuniverse / gamma
• Gamma = 1 / (1 – v2/c2)1/2
• If we want to travel to the stars the best
way is relativistic travel.
• Suppose we could travel such that
Gamma was equal to 1000 (yes that is
very close to the speed of light).
• If a star was 500 light years away how
long would it take to get there (hint, how
long does it take light to go that distance,
then divide by gamma)?
Pay the piper!
• The drawback is that a LOT of time
passes by on the earth.
• Going out 500 light years and coming back
might take only 1 year in the astronaut’s
time frame, but 1000 years still goes by for
the earth.
• And, 500 light years only gets you a small
ways into our galaxy let alone to another
galaxy.
Lorenz contraction
• Also, the sizes of moving objects are also
RELATIVE to their velocities in space.
• Linmotion = Lrest / gamma
• Gamma = 1 / (1 – v2/c2)1/2
• So (in the direction they are moving) their length
appears to shrink.
• However their other dimensions stay the same.
• A sphere for example would appear as a
saucer…
Conclusion
• Relativity is strange but cool, and not as
much math as you might think.
• Black holes are not vacuums.
• However, black holes do punch a hole
through space-time such that once you get
in (if you can do that) you can never leave!