Anandh Krishna Murichatta

Mathematical General Relativity

Lecture notes on the mathematical foundations of general relativity, from manifolds to the singularity theorems.

These notes follow Wald, Hawking and Ellis, and O’Neill. Notation and sign conventions are listed on the notes page.

Contents

  1. §1 Smooth manifolds and tensor fields in preparation
  2. §2 Connections, curvature & holonomy Jun 2026
  3. §3 Lorentzian geometry and causal structure in preparation
  4. §4 The Einstein equations as a PDE system in preparation
  5. §5 The Schwarzschild solution and global structure in preparation
  6. §6 Singularity theorems in preparation