General Relativity – An Introduction for Physicists

  • The spacetime of special relativity
  • Manifolds and coordinates
  • Vector calculus on manifolds
  • Special relativity revisited
  • Electromagnetism
  • The equivalence principle and spacetime curvature
  • The gravitational field equations
  • The Schwarzschild geometry
  • Experimental tests of general relativity
  • Schwarzschild black holes
  • Further spherically symmetric geometries
  • The Kerr geometry
  • The Friedmann–Robertson–Walker geometry
  • Cosmological models
  • Inflationary cosmology
  • Linearised general relativity
  • Gravitational waves
  • A variational approach to general relativity
    • Hamilton’s principle in Newtonian mechanics
    • Classical field theory and the action
    • Euler–Lagrange equations
    • Alternative form of the Euler–Lagrange equations
    • Equivalent actions
    • Field theory of a real scalar field
    • Electromagnetism from a variational principle
    • The Einstein–Hilbert action and general relativity in vacuo
    • An equivalent action for general relativity in vacuo
    • The Palatini approach for general relativity in vacuo
    • General relativity in the presence of matter
    • The dynamical energy–momentum tensor