A Most Incomprehensible Thing: Notes Towards a Very Gentle Introduction to the Mathematics of Relativity

Reader reviews
" ... do not be put off by the title! This is a great book on relativity which nicely bridges the gap between those books catering for readers who know little or nothing about relativity and those texts intended for physics mathematical specialists." - Amazon.co.uk

"Long story made short ... it is a gem. It works through the essential material and concepts carefully and patiently, and you would have a hard time not tracking the text, it is so clear. I highly recommend this book." - Amazon.com

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"Highly recommended for anyone willing to invest some time and effort." - Amazon.com

Teach yourself the mathematics of relativity
This book is aimed at the enthusiastic general reader who wants to move beyond the maths-lite popularisations in order to tackle the essential mathematics of Einstein's fascinating theories of special and general relativity. One of the cornerstones of modern physics, relativity is based on the concept of four-dimensional spacetime - curved in the vicinity of mass-energy, flat in its absence. Special relativity helps explain a huge range of non-gravitational physical phenomena and has some strangely counter-intuitive consequences. These include time dilation, length contraction, the relativity of simultaneity, mass-energy equivalence and an absolute speed limit. General relativity, the leading theory of gravity, is at the heart of our understanding of cosmology and black holes.

To paraphrase Euclid, there is no royal road to relativity - you have to do the mathematics, which undoubtedly has a somewhat daunting reputation. This introductory, self-study guide is for the lay reader who is motivated to tackle that challenge. The book is written using straightforward and accessible language, with clear derivations and explanations as well as numerous fully solved problems. 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 (which gives a good approximation of the spacetime of our Solar System); simple black holes, and what different observers would see if you were unfortunate enough to fall into one. Also covered are the mysteries of dark energy and the cosmological constant; plus relativistic cosmology, including the Friedmann equations and Friedmann-Robertson-Walker cosmological models. Following the historic 2015 LIGO detection, there is now also an additional chapter on gravitational waves.

Understand even the basics of Einstein's amazing theory and the world will never seem the same again.

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

This revised and corrected second edition now includes a new chapter on gravitational waves and a new appendix showing the derivation of the Riemann curvature tensor and some of its most important symmetries.