An Introduction to General Relativity (London Mathematical Society Student Texts, Series Number 5)

A lot of introductions to relativity are bigger than a small phone book, and they can chatter endlessly over points of obscure importance. This book is wonderfully concise, and that is both its great advantage and its slight downfall. I think of it as a most excellent---we can say superior---set of class notes from a most excellent---we can say superior---course. It shows you with great clarity what is important to the structure of the theory, and how to calculate with those important goodies. In such a tidy space, it doesn't have time to answer all the questions about the underlying "true meaning" of all the structures. It is a great field guide for someone to begin. It uses quite old indexed notation, which does have its use, although it can also obscure meanings. Whether used in lecture or for self-study, I think this would serve as the guide, and one or four other texts would be needed to augment the learning. Everything Woodhouse has out is good. I have a particular fondness for Ta-Pei Cheng's book at the beginning stage. At the next stage, I think that Wald and Choquet-Bruhat would be good follow on studies. It seems that much of what is insightful about relativity comes to us from the greater Oxford group of scholars. Go Oxford.

Read it carefully and go through every calculation yourself. That gives best experience.

Physicist E.A. Power writes: "excellent introduction for third-year undergraduates who are willing to work at learning the math as well as the physics." (Book Review, The Observatory, Vol. 111, Number 4,1991).I believe that assessment is accurate. Although slim (roughly 180 pages) this is an excellent introduction. It really is an introduction. If searching for a brief and readable account of General Relativity, along with the basic mathematical material, your search is over ! Armed with multivariable calculus and exposure to undergraduate-level physics, this book is within reach. One reason for perusal of this book is its excellent (and do-able) exercises. Read: "emphasis on the shorter type of problem that involves some thinking for its solution." Read, "Einstein's gravitational theory...is a subject of worthy intellectual enquiry...it is a work of art." 26 brief chapters. The metric convention here is (1,-1,-1,-1) opposite to the convention in Misner, Thorne and Wheeler's Gravitation. We learn: "The proper time experienced by a particle depends on the nature of the gravitational field through which it may be passing." (Page 8). Two brief sections entitled Matrix Algebra Made Easy and Vector Calculus Seen AFresh gets one through the morass ! Page 18 for the physicist elaborates upon utility of esu-units and setting c=1 for the study of electrodynamics. Excellent ! Chapter three, aspects of Special Relativistic Geometry, emphasizes light-cone structure and gives proper description of proper time ! (For instance, compare here to Frankel's chapter one exposition-- in his book Gravitational Curvature). We finish chapter three with a brief account of relativistic hydrodynamics. Every single exercise from these initial three chapters should be (and can be) successfully completed. Assiduous study of these initial 45 pages prepares the student for all that this textbook offers. The following four chapters (all of 25 pages) are mathematical: tensors, derivatives, curvature and Lie: "The Lie derivative has many uses in relativistic physics, it turns out often to be particularly helpful in reducing rather complicated looking tensorial expressions to simpler formulae, and in doing so giving them a heightened geometric content." (page 68). Also: "In relativity it is convenient to distinguish three layers of geometry: underlying manifold, the connection, the metric." (page 62). Two chapters elaborate upon geodesics and geodesic deviation. Next, differential forms. Exercise #11.6 (page 91) is delightful: "...the three-sphere can be represented as a pair of complex numbers...calculate the curvature in this basis." Then, physics again: "In finding Einstein's Equation...we shall be led by the geodesic hypothesis." Note this exercise: "Show that if the only energy in a region of space-time is electromagnetic, then the scalar curvature vanishes there." (page 100; comparing page 121 of Frankel: "A pure electromagnetic field curves space-time."). Chapter 14 is exceptional. Read: "Our development of General Relativity has been assisted by a series of assumptions motivated by analogy with special relativity and Newtonian gravitation. We must now check that we can indeed recover Newtonian Gravitation." A derivation of Schwarzschild solution proceeds in the following chapter. An exercise at the end of this chapter (fifteen) asks the reader "What is the maximum number of Killing vectors that an n-dimensional space can have ? " (page 108). This chapter, along with the next four, uncovers various applications of the Schwarzschild solution. Exercises (chapter 19) introduce the student to conformal metrics. Useful hints accompany many of the problems !. Interior Solutions, next. It is of some interest to compare this Chapter 21 to Frankel (his Chapter 11). Both authors are good and both are complementary (here elementary; Frankel advanced). The pinnacle here is Kerr solution, ending with brief discussion of the Penrose process (energy extraction): " the details are complex, but the reasoning behind this phenomenon is simple enough." We are then exposed to "the reasoning." We conclude with four chapters of cosmology. A job well done ! I have but one quibble: A paucity of references or bibliography.There you have it: at long last, a brief textbook which really is, as the title says, "an introduction" !Whether mathematics or physics student, it is hard to find a better compact presentation.Highly recommended !