Accelerated coordinates

General Relativity (Fall, 2008)

Lecture Playlist

  1. Newtonian Gravity and the equivalence principle

  2. Tidal forces and curvature

  3. Essential tools: tensors and the metric

  4. Tensor mechanics

  5. Covariant differentiation and geodesics

  6. The flat space of special relativity

  7. The Riemannian curvature tensor

  8. Equations of motion in curved space

  9. Gravitation in the Newtonian approximation

  10. Energy-momentum tensor and Einstein's equations

  11. Accelerated coordinates

  12. World lines and Schwarzschild solution

December 1, 2008

The integrated curvature depends only upon the topology of spacetime. (Euler number)

An accelerated observer coordinate drawn in a spacetime diagram traces hyperbolas. Rindler coordinates describe a uniformly accelerated coordinate frame. Rindler space has a horizon.

Birkhoff's theorem:  a spherically symmetric mass disbribution atracts as if the distribution was concentrated at a point. The solution to Einstein's equations outside a point is the Schwarzschild metric.

 

Topics: 
  • Local inertial coordinates
  • Rindler coordinates
  • Schwarzschild metric
  • Birkhoff's theorem
References