Energy-momentum tensor and Einstein's equations

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

November 24, 2008
The covariant divergence of the energy momentum tensor vanishes.
The covariant derivative of the metric tensor vanishes.
Einstein's equation in the Newtonian approximation.
Wave equation for a scalar field in curved space
Energy momentum tensor for the wave equation.
The cosmological constant adds an attraction or repulsion to Einstein's equation.
Topics: 
  • Wave equation
  • Energy momentum tensor
  • Cosmological constant
References