1. 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

2. Black Hole What is a black hole?

3. 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!

4. 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).

5. But there’s more! Mass warps space. Time is relative to space. Therefore masses warp time also! Tobject = Tuniversal / (1 – r s / r) 1/2 Where r s is the Schwarzschild radius (the radius of the event horizon of a black hole) r s = 1.5 km * Mass of object / Mass of our sun

6. 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.

7. 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).

8. 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)

9. 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!

10. 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 – v 2 /c 2 ) 1/2

11. Interstellar travel Tobject = Tuniverse / gamma Gamma = 1 / (1 – v 2 /c 2 ) 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)?

12. 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.

13. Lorenz contraction Also, the sizes of moving objects are also RELATIVE to their velocities in space. Linmotion = Lrest / gamma Gamma = 1 / (1 – v 2 /c 2 ) 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…

14. 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!