Goal: To get to know the ins and outs of relativity (relatively speaking) Objectives: To understand how Black holes compare to space-time To learn about General Relativity To learn about Special Relativity

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).

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

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…

Also From the perspective of anyone on the ship they are at rest (so ship is normal length). However, in the direction of “motion” the rest of the universe appears to be the one in motion Therefore the entire universe shrinks in the one direction and everything in it. So, the earth would look like a saucer as well.

Some other famous stuff You have probably heard that E = mc2 Too bad it is not completely correct… This is only the rest energy of matter. Yes, this means that matter is a form of energy!

However The total energy is E = Gamma mc2 And the kinetic energy is: KE = (Gamma – 1) mc2 So, most of relativity is multiplying or dividing by gamma!

That is all cool, but Why is it important? Space travel! We can go long distances – and in the lifetime of the astronauts. A 1000 light year trip at a gamma of 1000 would only take 1 year!

But what is the catch? The catch is 1000 years passes by for the universe and for the Earth. Lots of energy

Enormous Energy A 100 metric ton spacecraft traveling with a gamma of 1000 KE = (1000 – 1) * 105 kg * (3*108 m/s)2 KE = 9 * 1024 J USA currently uses 9.9 * 1019 J per year

So 1 spacecraft uses the energy we currently use in 90,000 years. In the future you would probably have hundreds to millions of these So, we will need about 1 trillion times the energy.

Conclusion Relativity is strange but cool, and not as much math as you might think. You basically just have to know how to find gamma, and apply that to everything.