Space-Time

4 dimensions: 3 space + 1 time

Has curvature: +, 0, -

Photons travel on geodesics

trajectories are called world lines

Event is marked by position (3 spatial coordinates) and time

each event has a light cone, which is the cone traced out by photons

Events can be

space-like: outside light cone

time-like: inside light cones

Special Relativity

Abandon all absolutes, you can only describe relative terms

No accelerations involved

Inertial reference frames

move at uniform velocity

laws of physics same in all IRFs

Two observers

co-moving observer

lab frame observer

Photon paths are straight lines

General Relativity

Add gravity to S.R.

IRFs are freely falling frames

an accelerating frame

elevator in free fall on Earth vs. elevator in empty space

Photon paths are curved geodesics

Gravity is the fact that space is curved around a mass

Black Holes

Space-time is very distorted

Nothing can get out of the Event Horizon

Extreme tidal forces

Observer far away never see traveler enter event horizon

T’s light is infinitely red-shifted