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 Edmund Bertschinger - MIT
Working with GR requires some understanding of differential geometry. In this text we will develop the essential mathematics needed to describe physics in curved spacetime. These notes assume familiarity with special relativity.
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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)
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