A First Course in General Relativity

  • Special relativity
  • Vector analysis in special relativity
  • Tensor analysis in special relativity
  • Perfect fluids in special relativity
    • Fluids
    • Dust: the number–flux vector N
    • One-forms and surfaces
    • Dust again: the stress–energy tensor
    • General fluids
    • Perfect fluids
    • Importance for general relativity
    • Gauss’ law
  • Preface to curvature
  • Curved manifolds
  • Physics in a curved spacetime
  • The Einstein field equations
  • Gravitational radiation
  • Spherical solutions for stars
  • Schwarzschild geometry and black holes
  • Cosmology