by Benjamin Crowell
Publisher: lightandmatter.com 2010
Number of pages: 334
This is an undergraduate textbook on general relativity. The book is meant to be especially 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.
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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.
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This course introduces the use of semigroup methods in the solution of linear and nonlinear (quasi-linear) hyperbolic partial differential equations, with particular application to wave equations and Hermitian hyperbolic systems.
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Smooth manifolds and scalar fields, tangent vectors, contravariant and covariant vector fields, tensor fields, Riemannian manifolds, locally Minkowskian manifolds, covariant differentiation, the Riemann curvature tensor, premises of general relativity.