An Introduction to General Relativity

  • Introduction
    • Space, time, and gravitation
    • The dynamics of the universe in its entirety
    • What is so special about general relativity?
    • The mercurial matter of Mercury
    • An idee fixe
    • Beside himself with joy
    • Rudis indigestaque moles
    • The metric tensor
    • The Levi-Civita connection
    • The field equations
  • Vectors and tensors in flat three-space
  • Aspects of special relativistic geometry
  • Tensor analysis on manifolds
  • Covariant differentiation
  • Properties of the Riemann tensor
  • Riemannian geometry
  • The Lie derivative
  • Geodesics
  • Geodesic deviation
  • Differential forms
  • The transition from Newtonian theory
  • Einstein’s field equations
  • The Schwarzschild solution
  • Gravitational red-shift and time dilation
  • The geodesic equation for the Schwarzschild solution
  • Classical tests
  • The extended Schwarzschild solution
  • Black holes and gravitational collapse
  • Interior solutions
  • The Kerr solution
  • Homogeneous and isotropic three-spaces
  • Cosmology: kinematics
  • Cosmology: dynamics
  • Anisotropic cosmologies