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Geometry and gravitation


  • Position of general relativity within physics
  • Equivalence principle
  • Spectral shift
  • Manifolds
  • Vector fields on manifolds
  • Tensor fields
  • Metric
  • Christoffel symbols
  • Normal coordinates
  • Geodesic equation
  • Schwarzschild metric
  • Nonrelativistic approximation
  • Killing vector fields
  • Perihelion advance, deflection of light, radar time delay
  • Curvature and torsion
  • Riemannian, Ricci tensor and curvature scalar, Einstein tensor
  • Energy-momentum tensor
  • Einstein's field equation
  • Cosmology, de-Sitter space-time, Friedmann equation, Friedmann models
  • Gravitational waves and their sources
  • Variational principles
  • U(1) theory, Yang-Mills theory, gauge theory of gravitation