Advanced General Relativity
by Neil Lambert
Publisher: King's College London 2009
Number of pages: 56
Contents: Introduction; Manifolds and Tensors; General Relativity (Derivation, Diffeomorphisms as Gauge Symmetries, Weak Field Limit, Tidal Forces: Geodesic Deviation, ...); The Schwarzchild Black Hole; More Black Holes; Non-asymptotically Flat Solutions.
Download or read it online for free here:
by Hermann Weyl - Methuen & Co.
A classic of physics -- the first systematic presentation of Einstein's theory of relativity. Long one of the standard texts in the field, this excellent introduction probes deeply into Einstein's general relativity, gravitational waves and energy.
by J.W. van Holten - arXiv
General relativity is outlined as the classical field theory of gravity, emphasizing physical phenomena rather than mathematical formalism. Dynamical solutions representing traveling waves and stationary fields of black holes are discussed.
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 Edward Witten - arXiv.org
This article is an introduction to causal properties of General Relativity. Topics include the Raychaudhuri equation, singularity theorems of Penrose and Hawking, the black hole area theorem, topological censorship, and the Gao-Wald theorem.