Mathematical problems of general relativity 1

  • Introduction
  • The laws of General Relativity
    • The Einstein equations
      • Regular ellipticity and regular hyperbolicity
    • The Cauchy problem
      • Cauchy problem for the Einstein equations: local in time existence and uniqueness of solutions
    • Decomposition of the Einstein equations
  • Asymptotic flatness at spacelike infinity and conserved quantities
  • The global stability of Minkowski spacetime
    • Statement of the problem
      • Field theories in a given spacetime
    • Sketch of the proof of the global stability of Minkowski spacetime