General Covariance and the Foundations of General Relativity
by John D Norton
Publisher: University of Pittsburgh 1993
Number of pages: 71
This text reviews the development of Einstein's thought on general covariance (the fundamental physical principle of his general theory of relativity), its relation to the foundations of general relativity and the evolution of the continuing debate over his viewpoint.
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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.
by J.W. van Holten - arXiv
General relativity is outlined as the classical field theory of gravity, emphasizing physical phenomena rather than mathematical formalism. Dynamical solutions representing traveling waves and stationary fields of black holes are discussed.
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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.
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The first half of the book is dedicated to developing the machinery of tensor calculus and Riemannian geometry required to describe physics in a curved space time. We will then turn to various applications of General Relativity.