Essential tools: tensors and the metric

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

October 6, 2008
Einstein summation convention.
Definition of an infinitesimal distance element.
Definition of a tensor.
Contravariant/covariant transformations.
Metric tensor defines the distance element.
Topics: 
  • Summation convention
  • Distance element
  • Contravariant
  • Covariant
  • Metric tensor
References