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General relativity


  • Motion in curved space
    • Metric tensor
    • Co- and contravariant vectors, tensors
    • Free particle in curvilinear coordinates
    • Parallel transport and covariant derivative
    • Geodesic coordinates
    • Motion in a gravitational field
    • Nonrelativistic approximation
  • Einstein's field equations
    • Geodesic deviation
    • Riemann's curvature tensor and Ricci tensor
    • Parallel transport and curvature
    • Energy-momentum tensor
    • Symmetric energy-momentum tensor
    • Energy-momentum tensor of an ideal fluid
    • Einstein's field equations
    • Action of the gravitational field
  • Static gravitational fields
    • Schwarzschild solution
    • Motion in the Schwarzschild metric
    • Experimental tests of general relativity
      • Spectral shift
      • Perihelion advance
      • Deflection of light
      • Radar time delay
      • Geodesic precession
  • Black holes
    • Singularities in the Schwarzschild metric
    • Space-time structure in Schwarzschild coordinates
    • Space-time structure in Eddington-Finkelstein coordinates
    • Space-time structure in Kruskal coordinates
    • Charged black hole
    • Rotating black hole
  • Gravitational waves
    • Linearized field equations
    • Plane waves
    • Polarization
    • Helicity
    • Generation of gravitational waves
  • Cosmology
    • Robertson-Walker line element
    • Friedmann equation
    • Friedmann models