Resources
A living list of books, notes and tools I find valuable.
Organised loosely by topic.
Foundations of GR#
- Wald — General Relativity. The standard graduate reference; rigorous and geometric.
- Misner, Thorne & Wheeler — Gravitation. Encyclopaedic; best for physical intuition.
- Hawking & Ellis — The Large Scale Structure of Space-Time. Global methods, causal structure, singularity theorems.
- O’Neill — Semi-Riemannian Geometry. The cleanest account of the underlying geometry.
The Einstein equations as PDE#
- Choquet-Bruhat — General Relativity and the Einstein Equations. The reference for the Cauchy problem.
- Ringström — The Cauchy Problem in General Relativity. Modern and self-contained.
- Chruściel — Elements of General Relativity. Excellent modern notes.
Causal structure & global methods#
- Penrose — Techniques of Differential Topology in Relativity.
- Beem, Ehrlich & Easley — Global Lorentzian Geometry.
Black holes & perturbations#
- Chandrasekhar — The Mathematical Theory of Black Holes.
- Dafermos & Rodnianski — Lectures on black holes and linear waves (arXiv:0811.0354).
Spinors & spin coefficients#
- Penrose & Rindler — Spinors and Space-Time, vols. 1–2.
- Stewart — Advanced General Relativity. A compact route to NP and GHP.
Numerical relativity#
- Alcubierre — Introduction to 3+1 Numerical Relativity.
- Baumgarte & Shapiro — Numerical Relativity.
Lectures online#
- Frederic Schuller — GR lectures — extremely clear mathematical foundations
- Sean Carroll — Lecture notes on general relativity
- PIRSA — Perimeter Institute recorded seminars
Tools#
- xAct (Mathematica) — tensor computer algebra; what I use most.
- Cadabra — field-theory-friendly computer algebra.
- SageManifolds — symbolic differential geometry in Python.
- Black Hole Perturbation Toolkit — codes and data for perturbation theory.