Tensors and Relativity: Chapter 6

Curved Spacetime and General Relativity

• Manifolds, tangent spaces and local inertial frames
• Covariant derivatives and Christoffel symbols
• Calculating from the metric
• Tensors in polar coordinates
• Parallel transport and geodesics
  • The variational method for geodesics
  • The principle of equivalence again
• The curvature tensor and geodesic deviation
  • The curvature tensor
  • Properties of the Riemann curvature tensor
• Geodesic deviation
• The Bianchi identities; Ricci and Einstein tensors
  • The Ricci tensor
  • The Einstein Tensor
• Index
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