A Most Incomprehensible Thing - Notes Towards a Very Gentle Introduction to the Mathematics of Relativity (2012)

Reader reviews (1) "Fantastic book ... very easy to follow and leads you gradually and gently to the full mathematical detail of general relativity." (2) "Highly recommended for anyone willing to invest some time and effort." - Amazon.com (1) " ... 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." (2) "A new gold standard for physics books." (3) "A unique book. Well done the author." - Amazon.co.uk Synopsis Based on the concept of four-dimensional spacetime - curved in the vicinity of mass-energy, flat in its absence - Einstein's theories of special and general relativity together form a cornerstone of modern physics. Special relativity has some strangely counter-intuitive consequences, including time dilation, length contraction, the relativity of simultaneity and mass-energy equivalence, whilst general relativity is at the heart of our understanding of black holes and the evolution of the universe. Using straightforward, accessible language, 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. (To paraphrase Euclid, there is no royal road to relativity - you have to do the mathematics.) 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 Einstein field equations; the Schwarzschild solution; the four classical tests of general relativity; simple black holes; the mysteries of dark energy and the cosmological constant; and the Friedmann equations and Friedmann-Robertson-Walker cosmological models. 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 Bibliography Appendix - Planetary motion data Acknowledgements Table of contents......Page 2 Preface......Page 12 Introduction......Page 16 1 Foundation mathematics......Page 21 2 Newtonian mechanics......Page 112 3 Special relativity......Page 150 4 Introducing the manifold......Page 230 5 Scalars, vectors, one-forms and tensors......Page 240 6 More on curvature......Page 271 7 General relativity......Page 303 8 The Newtonian limit......Page 339 9 The Schwarzschild metric......Page 354 10 Schwarzschild black holes......Page 403 11 Cosmology......Page 430 Bibliography......Page 476 Appendix......Page 478 Acknowledgements......Page 482