Based on the notion of four-dimensional spacetime, Einstein's theories of special and general relativity together form a cornerstone of modern physics. With numerous fully solved problems and clear derivations and explanations, this book is aimed at the enthusiastic general reader who wants to move beyond maths-lite popularisations and tackle the essential mathematics of this fascinating theory. For those with minimal mathematical background, the first chapter provides a crash course in foundation mathematics. The reader is then taken gently by the hand and guided through a wide range of fundamental topics, including Newtonian mechanics; the Lorentz transformations; tensor calculus; the Schwarzschild solution; simple black holes; dark energy and the cosmological constant; the Friedmann equations and Friedmann-Robertson-Walker cosmological models; and gravitational waves. Understand even the basics of Einstein's amazing theory and the world will never seem the same again. January 2019 - updated EPUB edition.
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Table of Contents
Preface; Introduction; 1-Foundation mathematics; 2-Newtonian mechanics; 3-Special relativity; 4-Introducing the manifold; 5-Scalars, vectors, one-forms and tensors; 6-More on curvature; 7-General relativity; 8-The Newtonian limit; 9-The Schwarzschild metric; 10-Schwarzschild black holes; 11-Cosmology; 12-Gravitational waves; Appendix: The Riemann curvature tensor; Bibliography; Acknowledgements