General Relativity Notes
by Edmund Bertschinger
Publisher: MIT 1999
Number of pages: 156
Working with GR, particularly with the Einstein field equations, requires some understanding of differential geometry. In this text we will develop the essential mathematics needed to describe physics in curved spacetime. These notes assume familiarity with special relativity.
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by Neil Lambert - King's College London
Contents: Introduction; Manifolds and Tensors; General Relativity (Derivation, Diffeomorphisms as Gauge Symmetries, Weak Field Limit, Tidal Forces, ...); The Schwarzchild Black Hole; More Black Holes; Non-asymptotically Flat Solutions.
by Benjamin Crowell - lightandmatter.com
This is an undergraduate textbook on general relativity. It is well adapted for self-study, and answers are given in the back of the book for almost all the problems. The ratio of conceptual to mathematical problems is higher than in most books.
by Shlomo Sternberg
Course notes for an introduction to Riemannian geometry and its principal physical application, Einstein’s theory of general relativity. The background assumed is a good grounding in linear algebra and in advanced calculus.
by Giampiero Esposito - arXiv
An attempt is made of giving a self-contained introduction to holomorphic ideas in general relativity, following work over the last thirty years by several authors. The main topics are complex manifolds, spinor and twistor methods, heaven spaces.