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Gravitational Curvature: An Introduction to Einstein's Theory by Theodore Frankel (Paperback, 2011)

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This classic text and reference monograph applies modern differential geometry to general relativity. A brief mathematical introduction to gravitational curvature, it emphasizes the subject's geometric essence, replacing the often-tedious analytical computations with geometric arguments. Clearly presented and physically motivated derivations express the deflection of light, Schwarzchild's exterior and interior solutions, and the Oppenheimer-Volkoff equations. A perfect choice for advanced students of mathematics, this volume will also appeal to mathematicians interested in physics. It stresses the global aspects of cosmology and is suitable for independent study as well as for courses in differential geometry, relativity, and cosmology. Prerequisites include a background in Riemannian geometry and basic physics or a familiarity with relativity theory. Background chapters, with derivations, cover special relativity, continuum mechanics, and electromagnetism.