The Mathematical Theory of Relativity
by Arthur Stanley Eddington
Publisher: Cambridge University Press 1923
Number of pages: 448
Sir Arthur Eddington here formulates mathematically his conception of the world of physics derived from the theory of relativity. The argument is developed in a form which throws light on the origin and significance of the great laws of physics; its consequences are followed to the full extent in the consideration of gravitation, relativity, mechanics, space-time, electromagnetic phenomena and world geometry.
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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 Sean M. Carroll
General relativity has a reputation of being extremely difficult. This introduction is a very pragmatic affair, intended to give you some immediate feel for the language of GR. It does not substitute for a deep understanding -- that takes more work.
by Eric Gourgoulhon - arXiv
These notes introduce the theory of rotating stars in general relativity. The focus is on the theoretical foundations, with a detailed discussion of the spacetime symmetries, the choice of coordinates and the derivation of the equations of structure.
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.