The Riemannian curvature tensor

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 3, 2008
Parallel transport in curved space.
A gyroscope parallel transports it's axis of spin.
Define the Riemann curvature tensor and the Ricci tensor.
In general relativity, mass alters geometry, and curved geometry deflects mass from moving in a straight line.
The continuity equation for charge.
The continuity equation for 4-momentum is the vanishing divergence of the energy momentum tensor.
Topics: 
  • Parallel transport
  • Riemann curvature tensor
  • Ricci tensor
  • Continuity equation
  • Energy momentum tensor
References