Goal: To get to know the ins and outs of relativity (relatively speaking) Objectives: 1)To understand how Black holes compare to space-time 2)To learn about General Relativity 3)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 – 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

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).

Journey into a black hole Is it possible or advisable? The answer to the first is NO Time stops for you before you can make it into the black hole So, the black hole has to come to you. Is it advisable, talk about that during black hole lecture

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

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…

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.

But what happens… If you are traveling a fraction of the speed of light and something flies by you? First, a conceptual question, suppose light goes by you when you are traveling 90% of the speed of light. What velocity does the light appear to be traveling?

But what happens… If you are traveling a fraction of the speed of light and something flies by you? First, a conceptual question, suppose light goes by you when you are traveling 90% of the speed of light. What velocity does the light appear to be traveling? - the speed of light! Light always appears to go the speed of light in a vacuum! This is why lengths contract and time slows down. If earth was watching though, they would see light move past you at 0.1 c faster than you…

Some other famous stuff You have probably heard that E = mc 2 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 mc 2 And the kinetic energy is: KE = (Gamma – 1) mc 2 And momentum is: p = gamma * mv 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.

How do we know relativity is real? 1) Particles created in the upper atmosphere make it to the surface even though their lifetimes are much shorter than the time it takes them to get to the Earth The time dilation allows them to live longer in our time frame as their half lives are for their time frame

2) Mercury By the early 20 th century it was known that Mercury seemed to lag 37 arcseconds behind in its orbit per century from what the Kepler model predicted. The faster orbit and being closer to the sun make its clock run a little slower Relativity was the cause of this

3) Satellites Since they are further out of Earth’s gravity well their clocks run a tiny bit slower So, their clocks have to be adjusted by about a millisecond per year. All as predicted by relativity.

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.