Introduction to General Relativity
by Gerard 't Hooft
Publisher: Rinton Press 2010
Number of pages: 69
This book presents, in a natural and beautiful way, the general relativity as a scheme for describing the gravitational field and the equations it obeys. Starting from physical motivations, curved coordinates are introduced, and then the notion of an affine connection field is added. At a later step, the metric field is added. One then sees clearly how space and time get more and more structure, until finally Einstein's field equations logically come out.
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by Horst R. Beyer - arXiv
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.
by Arthur Stanley Eddington - Cambridge University Press
The author gives an account of general relativity theory without introducing anything very technical in the way of mathematics, physics, or philosophy. It is hoped that the book may also appeal to those who have gone into the subject more deeply.
by Francis Dominic Murnaghan - Johns Hopkins press
This monograph is the outcome of lectures delivered to the graduate department of mathematics of The Johns Hopkins University. Considerations of space have made it somewhat condensed in form, but the mode of presentation is sufficiently novel.
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.