an advanced course in general relativity

  • Fundamentals
  • Geodesic Congruences
  • Hypersurfaces
  • Lagrangian and Hamiltonians of General Relativity
  • Black holes
    • Schwarzschild black hole
    • Reissner-Nordstrom black hole
    • Kerr black hole
      • The Kerr metric
      • Dragging of inertial frames: ZAMOs
      • static limit: static observers
      • Event horizon: stationary observers
      • The Penrose process
      • Principal null congruences
      • Kerr-Schild coordinates
      • The nature of the singularity
      • Maximal extension of the Kerr spacetime
      • Surface gravity
      • Bifurcation two-sphere
      • Smarr’s formula
      • Variation law
    • General properties of black holes
    • The laws of black-hole mechanics