Covariant differentiation and geodesics

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 20, 2008

Transformation properties of tensors are most important.
Covariant differentiation transforms covariantly.
The covariant derivative of the metric tensor vanishes.
Construct the Christoffel symbol from the metric tensor.
A geodesic curve is defined as the curve tangent to itself.
Particles in space move along geodesics.

Topics: 
  • Covariant derivative
  • Christoffel symbol
  • Geodesic
References