This compact guide presents the key features of general relativity, to support and supplement the presentation in mainstream, more comprehensive undergraduate textbooks, or as a re-cap of essentials for graduate students pursuing more advanced studies. It helps students plot a careful path to understanding the core ideas and basics of differential geometry, as applied to general relativity, without overwhelming them. While the guide doesn't shy away from necessary technicalities, it emphasises the essential simplicity of the main physical arguments. Presuming a familiarity with special relativity (with a brief account in an appendix), it describes how general covariance and the equivalence principle motivate Einstein's theory of gravitation. It then introduces differential geometry and the covariant derivative as the mathematical technology which allows us to understand Einstein's equations of general relativity. The book is supported by numerous worked exampled and problems, and important applications of general relativity are described in an appendix.
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Table of Contents
Preface; 1. Introduction; 2. Vectors, tensors and functions; 3. Manifolds, vectors and differentiation; 4. Energy, momentum and Einstein's equations; Appendix A. Special relativity - a brief introduction; Appendix B. Solutions to Einstein's equations; Appendix C. Notation; Bibliography; Index.