general relativity – concide introduction

  • Gravity as geometry
  • Geodesics
    • Straight lines and great circles
    • Spacetime and causal structure
    • The metric
    • The geodesic equation
    • The Newtonian limit
  • Geodesics in the Solar System
    • The Schwarzschild metric
    • Geodesics in the Schwarzschild metric
    • Planetary orbits
    • Light detection
    • Shapiro time delay
    • Gravitational red shift
    • The PPN formalism
  • Manifolds and Tensors
  • Derivatives and Curvature
    • Integration
    • Why derivatives are more complicated
    • Derivatives of -forms: Cartan calculus
    • Connections and covariant derivatives
    • The Christo el/Levi-Civita connection
    • Parallel transport
    • Curvature
    • Properties of the curvature tensor
    • The Cartan structure equations
  • The Einstein Field Equations
    • Gravity and geodesic deviation
    • The Einstein-Hilbert action
    • Conservation laws
    • Generalizing the action
  • The Stress-energy Tensor
    • Energy as a rank two tensor
    • The stress-energy tensor for a point particle
    • Perfect Fluids
    • Other Fields
    • 7.5 Di fferential and integral conservation laws
    • 7.6 Conservation and the geodesic equation
  • The Weak Field approximation
  • Gravitational Waves
  • Black Holes
  • Cosmology
  • The Hamiltonian Formalism
  • Next steps
  • Appendix A Mathematical details
    • Manifolds
    • Maps between Manifolds
    • Topologies
    • Cohomology
    • Integrals of -forms and Stokes’ Theorem
    • Curvature and holonomies
    • Symmetries and Killing vectors
    • The York decomposition