Einstein's Theory: A Rigorous Introduction for the Mathematically Untrained

This is an outstanding book on a subject that many authors have failed to portray adequatly.I have read many books on Einstein's theories and until completing this offering was in a state of confusion having been left with many unanswered questions and a subsequent feeling of inadequacy on my part as a reader. It would seem that Eddington's quoted statement in the preface that mathematical physics cannot be understood by popularisation has proved true - intelligent readers will be left baffled by such attempts. I don't claim to be intelligent but I have certainly been baffled by countless other books on the subject - including Einsteins own attempt to explain things without recourse to maths!This book introduces all the mathematics necessary to acquire a level of understanding of the treatment of non-euclidean geometries thereby providing the foundations necessary to give the concise formulation of the Einstein field equations. This is achieved by educating the reader in vectors, differential and integral calculus, vector transformations, contravarient and covariant vectors, curvilinear coordinates systems and tensors. In order to achieve an understanding of intrinsic curvature Christoffel symbols and parallel transport are introduced which leads into the Riemann, Ricci and Einstein tensors. Along the way the authors describe philosophical difficulties that along with the deeper understanding of the maths resolve many of the questions that arise from less satisfactory treatments of the subject.I found the treatment of rotating reference frames and the related subject on gravitational time dilation to be outstanding - possibly as a result of a newly acquired understanding of the maths necessary to describe these complex situations. Similarly the concise treatment of some of the common solutions to the field equations and the predictions of the theory are a testament to the success of the authors approach. Indeed less than a third of the book, 100 odd pages, covers the theory itself, the field equations and their solutions, predictions, black holes, and cosmological implications including inflation! All of these subjects are completely amenable thanks to the remarkable mathematical tuition offered by the previous two thirds of the book.I compliment and whole heartedly thank the authors for this work. I cannot recommend it enough.

All new and difficult concepts are crystal-clear explained. I only disagree with the subtitle about ' the mathematically untrained' that will surely be unable to go throughout the entire text. All students studying the subject of Einstein's Theory on relativity should have a wonderful companion in this book.