A General Relativity Workbook

For decades, I was a professor doing ultrafast laser spectroscopy and teaching courses in quantum mechanics, molecular spectroscopy, and thermodynamics. After retiring several years ago, I started to explore unfamiliar areas in physics. Fortunately, the last few years have seen the emergence of several entry-level texts from highly talented educators – Griffiths’ Introduction to Elementary Particles, Zwiebach’s A First Course in String Theory, Carroll and Ostlie’s An Introduction to Modern Astrophysics, Ryden’s An Introduction to Cosmology, Aitchison and Hey’s Gauge Theories in Particle Physics, and Taylor and Wheeler’s Spacetime Physics. All of these have given me many hours of enjoyment, working through problems and gaining new insights.In my view, Thomas Moore’s A General Relativity Workbook ranks right up there with the best of them. Ryden’s cosmology book won the inaugural Chambliss Astronomical Writing Award of the American Astronomical Society, and I feel that Moore’s new book is highly deserving of similar recognition. I am well aware that Moore has received checkered reviews from Amazon readers, and I will address the reasons for this at the end of this review.Moore’s format is admittedly unorthodox, patterned somewhat after Taylor and Wheeler. Each of the 39 chapters typically opens with 4 pages of text. These pages of text tend to resemble abstracts rather than standard text in a typical physics book, and they are not generally understandable upon first reading. Comprehension only begins to emerge in the group of Exercises that follows the text in each chapter. The derivations of key equations in the text are dissected in these Exercises, grouped together in modules called Boxes. (The latter term is reminiscent of similarly termed sections in Misner, Thorne and Wheeler’s Gravity, a 1200-page dreadnought jocularly called the Telephone Book.) Moore’s boxes are an invaluable component: their careful, step-by-step guidance to the standard equations in GR saves countless student-hours of replicating results that are given without proof in more advanced texts. Physical insight finally begins to crystallize in the symbiosis of going back and forth between the text and the Exercises. The Boxes allot blank spaces for working these Exercises, and the pages are perforated, presumably so that people can hand in their solutions to the Exercises. I did not write my solutions in these Boxes: many of those spaces would have been fairly cramped, and their printed content (which explains how to do the Exercises) is far too valuable to be thrown away. Instead, I wrote my solutions to the Exercises and Problems separately in a notebook, accumulating some 600 handwritten pages by the end of Chapter 39. Each chapter ends with several Homework Problems. Most of these are beautifully crafted; some are adaptations of problems from other GR texts, but redesigned to ensure logical connectivity to the body of the text and Boxes. Few of these Problems are superfluous. All of them are geared to establishing an important physical point. Many of the Problem statements are augmented with discussions of the physical significance of the results. The Problems are tightly organized in an overarching way: for example, the use of spacetime diagrams that Moore encourages in several of the Problems in Chapter 2 facilitate understanding the Kruskal-Szekeres diagrams in Chapter 15. The correct solutions to many of the more difficult problems in earlier chapters have a way of turning up in later chapters; with patience, students will eventually learn those solutions as they work toward the end of the book. (For example, the electromagnetic stress-energy tensor requested in Problem P7.8 is eventually revealed in the statement of Problem P23.4.) This feature enhances the book’s usefulness in self-study, but it will not be discovered if a student turns away in frustration early on.Why do I regard this book so highly? First, Moore has a gift for language that few other scientists have; he has a keen sense for what it feels like not to understand GR or its mathematical foundations in tensor calculus. His discussions have a strongly physical rather than mathematical bent. His description of the physical origin of the Mercury’s precession of the perihelion is beautifully done, as is his account of the Local Flatness Theorem in Box 17.7. His historical narratives (like Einstein’s encounters with the cosmological constant) are superb, and the book is liberally sprinkled with references to original sources for things like the Reissner-Nordholm solution for a charged black hole. As one works out solutions to many of the more advanced Problems, physical insights will often jump out in technicolor. An example of the latter happened when I obtained the weak-field gravitomagnetic Fij matrix around a rotating star in Problem P22.5: the resulting expressions formally resemble those for the familiar field around a magnetic dipole! (Appreciating this, however, does require prior knowledge of classical EM theory.) The treatment of gravitational waves is particularly well done, perhaps because Moore has been personally involved in the LISA project. Upon first learning about the related LIGO project in another GR text, I could not understand how the potential value of such a project justified its enormous expense. I do understand it now. Finally, a real test of the book’s worth is whether it can provide a bridge to more advanced books like Hartle’s Gravity. For me, Hartle (as well as parts of the Telephone Book) came alive only after I went through Moore. In comparison to Hartle, Moore is remarkably free of typos – a huge feat of proofing, given that the indices in the Christoffel coefficients and Riemann tensors are seemingly as ubiquitous as neutrinos. A relatively short list of known typos is available on the workbook’s website.Why, then, are the Amazon reviews of Moore so disparate? The most critical comments stem from the unavailability of solutions to the Exercises and/or Problems. Moore does require a good working knowledge in algebra, trigonometry, calculus, some familiarity with ordinary differential equations and linear algebra, and a solid feel for the elementary physics (Newtonian mechanics and classical electromagnetism) covered in the first 2-3 years of undergraduate study. Some students who emerge from these courses will have had enough curiosity and initiative to develop these tools; some will not. Moore presupposes very little beyond this elementary background; he develops the required tensor algebra and calculus (absolute gradients etc.) entirely from scratch. In my dealings with advanced undergraduate and first-year graduate students over the years, I encountered many who would have had little difficulty with most of Moore’s Problems. For a well-prepared student, I feel Moore is a superb text for self-study. Its “workbook” format may have misled some readers into expecting an Idiots’ Guide to GR, which of course it is not.

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Thomas Moore's introduction to general relativity is superb. It gives an accessible introduction to the subject at an elementary level. I'd like to keep this review brief, so let me just mention some important points prospective readers may want to know.1. Pre-requisites are kept to a minimum. All one needs is familiarity with basic vector calculus, and an introductory course on mechanics and electromagnetism. The Lagrangian based treatment of mechanics at the level of John Taylor's book would be beneficial, but not essential. Similarly, Electromagnetism at the level of David Griffiths' book would be beneficial, but not essential. The essential mathematics and physics are systematically developed throughout the textbook.2. The book format consists of 39 chapters. Each chapter starts out with roughly 4 pages of introductory material, followed by exercises labeled "Box Exercises" where the student is asked to fill in incomplete arguments in the introduction, and the chapter concludes with a set of more advanced homework problems, with about 10 problems per chapter.3. The book includes an online student manual found at the instructor's Pomona webpage. The manual contains answers to many of the Box exercises, and hints or partial solutions to many of the homework problems. The student should be able to know whether they have found correct solutions to most of the box problems and homework problems. The student manual and the systematic student guide of the mathematics and physics requiring minimal prerequisites makes this textbook suitable for self-study.

Getting started in GenRel is not easy. I still believe that MTW is the "gold standard" in the field. However, in the absence of an exceptionally strong background in physics and mathematics, going directly to MTW is not a realistic goal. Undergraduates need a solid foundation before tackling a grad course, and those pursuing self study need the same. This text is the answer! It provides an exceptional base of information in GenRel that would serve an undergrad or someone pursuing self-study exceptionally well. This text leads the learner through an entire basic course in GenRel, each chapter logically developing each topic. There is a plethora of problems to solve that are presented in a clear and logical manner. Solving the problems is the only way to learn GenRel. This book is the best thing going for people starting out to learn GenRel. The "workbook" concept is a great idea (I think this is the only GenRel workbook out there) and Moore carries it out perfectly! The only thing missing is a Solutions Manual for the person engaged in self-study.

An amazing book for introducing the concepts of General relativity. The author is very good at guiding the reader through the mathematics and concepts introduced in general relativity. He is able to explain the mathematics and introduces New mathematics such that anyone who has completed a second year course in mathematics can understand how it is properly used and when to use it. I highly recommend this book to anyone who is interested in learning general relativity.

If you are zero order in general relativity and would like to know about this topic in deep, this book is what you want for sure ! Moreover, whether you're willing to come along in this journey of different formalism of tensor calculus as well as general relativity take it on and you won't be regretted !Enjoy it because I've already been enjoying it !

I read some of the criticisms; I generally don't expect the kind of perfection described, especially if I am in the practice for learning mode. This book helps me very effectively and as far as I can tell nothing is out there competing with this approach.