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The Geometry of Physics by Theodore Frankel

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CHAPTER 11

Relativity, Tensors, and Curvature

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11.1. Heuristics of Einstein’s Theory

What does g00 have to do with gravitation?

11.1a. The Metric Potentials

Einstein’s general theory of relativity is primarily a replacement for Newtonian gravitation and a generalization of special relativity. It cannot be “derived”; we can only speculate, with Einstein, by heuristic reasoning, how such a generalization might proceed. His path was very thorny, and we shall not hesitate to replace some of his reasoning, with hindsight, by more geometrical methods.

Einstein assumed that the actual space-time universe is some pseudo-Riemannian manifold M4 and is ...

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