general relativity

extends special relativty by including the effect of gravity

equivalence principle

• free falling in gravity ~ free floating in space
• standing in gravity ~ an accelerating frame

Friedmann-Lemaitre-Robertson-Walker spacetime

• Space is homogeneous and isotropic
• Space is uniformly filled with matter

mass warps spaccetime

• Schwarzschild radius, r_s = 2GM/c^2
• (ds)^2 = (1 - r_s/r)(cdt)^2 - (1 + r_s/r)(dx)^2
• time slows in curved space time
  • consider a clock on a rotating space station with artifical gravity

curvature of time causes gravity

• time curvature dominates for weak gravitational field and objects at low velocity
• see Newtonian limit

why does mass warp light

• light has no velocity in the time dimension
• consider a space ship shooting a laser perpendicular to its motion
  • to the outside observer the light moves in a straight line
  • to the inside observer the light moves in a curve

inconsistent with quantum mechanics

• in QM a particle can be in multiple places, what happen to its gravity?

refs

• The Maths of General Relativity
• General Relativity Without Calculus
• General Relativity from A to B