The Geometry of General Relativity
by Tevian Dray
Publisher: Oregon State University 2014
Number of pages: 158
The manuscript emphasizes the use of differential forms, rather than tensors, which are barely mentioned. The focus is on the basic examples, namely the Schwarzschild black hole and the Friedmann-Robertson-Walker cosmological models. The material should be suitable for both advanced undergraduates and beginning graduate students in both mathematics and physics.
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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 Nikodem J. Poplawski - arXiv
A self-contained introduction to the classical theory of spacetime and fields. Topics: Spacetime (tensors, affine connection, curvature, metric, Lorentz group, spinors), Fields (principle of least action, action for gravitational field, matter, etc)
by Arthur Stanley Eddington - Cambridge University Press
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.
by Gerard 't Hooft - Rinton Press
The book presents 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.