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.
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The author presents the pedagogical introduction to relativistic astrophysics and cosmology, which is based on computational and graphical resources of Maple 6. The knowledge of basics of general relativity and differential geometry is supposed.
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The status of experimental tests of general relativity and of theoretical frameworks for analyzing them are reviewed and updated. Tests of general relativity have reached high precision, including the light deflection, the Shapiro time delay, etc.
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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.