Advanced Lectures on General Relativity

  • Surface Charges in Gravitation
  • Three Dimensional Einstein’s Gravity
  • Asymptotically Flat Spacetimes
    • A Definition of Asymptotic Flatness
      • Asymptotic Structure of Minkowski Spacetime
      • Gravity in Bondi Gauge
      • Initial and Late Data
    • Asymptotic Symmetries: The BMS4 Group
      • Supertranslations
      • Lorentz Algebra and Its Extensions
      • Gravitational Memory Effects
  • Rotating Black Holes
    • The Kerr Solution: Review of the Main Features
      • Metric in Boyer-Lindquist Coordinates
      • Killing Horizon and Black Hole Thermodynamics
      • Ergoregion
    • Extremal Rotating Black Holes
    • Black Hole Spectroscopy