A most incomprehensible thing : notes towards a very gentle introduction to the mathematics of relativity / Peter Collier. - Second edition - 339 pages : illustrations ; 24 cm.
Foundation mathematics --
Newtonian mechanics --
Special relativity --
Introducing the manifold --
Scalars, vectors, one-forms and tensors --
More on curvature --
General relativity --
The Newtonian limit --
The Schwarzschild metric --
Schwarzschild black holes --
Appendix A. Planetary motion data --
Appendix B. The Riemann curvature tensor.
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 (in plain English: very weird) consequences. These include time dilation, length contraction, the relativity of simultaneity, mass-energy equivalence and an absolute speed limit. General relativity, a 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. This introductory, self-study guide 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; simple black holes (and what different observers would see if someone was 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. Understand even the basics of Einstein's amazing theory and the world will never seem the same again.
530.15 / C6995m 2014