A General Relativity Workbook

Clear and well organised book

The book's chapters are separated into 9 main topics or sections, if the introduction can be counted as a "topic", these are: Introduction, Flat Spacetime, Tensors, Schwarzschild Black Holes, The Calculus of Curvature, The Einstein Equation, Cosmology, Gravitational Waves, and Spinning Black Holes. These sections are not listed in the Contents, only the names of the chapters are listed there, however the section names and the chapters within each section are listed in the Preface where a very useful flow diagram is given which explains how each of the sections depend on one another. This means you don't necessarily have to read the book linearly, although I did, and the splitting into named sections also helps to keep your focus on what you're trying to achieve when studying the relevant chapters. The author and the publishers, University Science Books, clearly listened to the valid criticism that the book was of little use for self study since it didn't contain any solutions or hints to the exercises - as since 2013 the author has made available an online manual, which is downloadable as a pdf file from the book's web page or the publisher's web site. The manual contains "Hints, Tips and Short Answers to Selected Problems" and so, although no full solutions are given, there are hints to how a particular exercise could be approached and/or the final answer to the exercise. Although full solutions would have been better for those using the book for self study, it would have made the book useless for lecture courses, and so the production of this manual of tips and short answers seems to be a balanced response from the author who genuinely seems to be trying to help those reading the text for self study as much as he's able in the circumstances.

This offers one of the best introductions to General Relativity. What sets this apart is that it is a workbook, leaving blank spaces for the student to complete proofs/examples or/and do exercises that the reader must absolutely must do. I find this to be a very effective way to learn something (provided that you have the skill to fill-in everything that the book asks you to) because it makes sure that the reader is never reading through it passively (reading but not thinking and/or understanding). The only possible drawback is that every once in a while the reader might not be able to complete an important proof, but that depends on the skill and determination of the reader and is to be expected from a workbook so I will not hold this against it (you already know what you are getting into before buying this). A reader can use this for a main book and supplement it with one of the many excellent textbooks on General Relativity (such as Zee's "Einstein Gravity in a Nutshell") for more detailed discussions on the material presented here and also for the rare proof and/or exercise/example that the reader might not find a way to complete.

I am a physics professor and I find this book to be very well suited for use in an undergraduate GR course. The author gave a lot of thoughts about structuring the material and as a result the book offers an excellent support for teaching a GR course at different levels. Interdependencies of the chapters are kept to a minimum and so depending on student's level the sequence of the course can be easily changed as well as the most difficult parts omitted without sacrificing the logic of the course. I also find the balance between descriptive material and the excercize-oriented one very reasonable, and most of the explanations of the basics concepts are very clear. The main (and rather serious) flaw of the book is its binding. It is weak, a crease formed after a few days of use. It later developed into a large crack and I had to glue the two parts of the book together. It is not a cheap book, especially for students, and it is a pity that the publisher cuts corners.

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.

Recebi ontem à tardinha. Depois de lido terei condições de fazer uma avaliação sensata do livro. Mas posso adiantar que , verificando o índice, o livro cobre todos os assuntos, tais como, revisão de relatividade especial (capítulo 1), 4-vetores (capítulo 2), Termodinâmica de buracos negros (capítulo 16), Evolução do Universo (capítulo 26), Astronomia de ondas gravitacionais (capítulo 34), o Universo primitivo (capítulo 32), etc. Os outros capítulos cobrem assuntos que normalmente são estudados em todo livro de Relatividade. São 39 capítulos cobrindo todos os assuntos relevantes e atuais da relatividade geral, em 476 páginas, em nível de último ano de graduação de Física.

内容は大学院レベルと思われるが，最近の観測事実を取り入れ，Einsteinの理論を発展させた内容となっている。天体物理方面の勉強を目指している学生にとっては，便利で基本的な入門書と思う。

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.