The Riemannian curvature tensor

General Relativity (Fall, 2008)

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.
  • Parallel transport
  • Riemann curvature tensor
  • Ricci tensor
  • Continuity equation
  • Energy momentum tensor