Gravity: An Introduction to Einstein's General Relativity

"This is an excellent introduction to general relativity with a hands-on approach that is based on physical situations of interest like black holes and the expanding universe. It fills a real gap in the literature for an undergraduate or graduate student course book" - Stephen HawkingHartle's "Gravity" is a textbook for learning general relativity. On the back cover of the book, there are a lot of praises for the book from famous physicists including Stephen Hawking's.Overall, I enjoyed the book and the reading was beneficial. The book contains many topics with detailed explanations in more than 500 pages. Considering that, as the author says in the preface, the book aims at guiding undergraduate students to general relativity, its plentiful explanations are great merits. However, the book has some shortcomings. If you feel comfortable only with mathematics textbooks that are written logically and systematically, then the book can be uncomfortable for you.The book consists of three parts. The first part introduces the readers to the basics of relativity only with elementary mathematics. The second part is about applications of relativity. For example, the book explains how general relativity explains motions of solar system by showing that Newtonian mechanics is an approximation of general relativity that can explain things more accurately. In addition, light rays under gravitational field, gravitational waves, black holes, and cosmology are discussed under the relativistic point of view.But when we use general relativity in the first two parts to analyse real physical situations, that does not mean we solve problems directly from the Einstein equation. There is a special solution of the Einstein equation, called Schwarzschild metric. By applying this metric to situations like planets in solar system and black holes, we study those things.The third part introduces the Einstein equation and its related mathematics. However, even in this part, we don't solve the Einstein equation. Solving the Einstein equation explicitly seems to be a hard thing.As I mentioned, the book's explanation is confusing in many places. For example, it is when introducing new mathematical stuffs like scalar product in the first part, and Christoffel symbols and covariant derivatives in the third part. Before reading the book, I have read two relativity books, Peter Collier's, and Ellis and Williams's. In reading such parts, the experience of reading the two books were really helpful. In particular, Collier's book was good.For the third part, I just can give three or four stars. I think that the mathematics like covariant derivative and Riemann curvature tensor is neither easily explained nor dealt with in depth. I have a plan to read another relativity book like Foster and Nightingale's "A Short Course in General Relativity". But for the first two parts, although there are many confusing parts, I want to give them five stars. They contain many valuable topics. I want to give an example.Consider a non-rotating black hole. Then the geometry around the black hole is described by a global coordinate (t, r, theta, phi) with a metric called the Schwarzschild metric. The motion of a particle can be described by (t(time), r(time), theta(time), phi(time)). The particle has some energy and momentum. Suppose I am in a rocket moving around the black hole. My motion will be described by (t'(time), r'(time), theta'(time), phi'(time)). To me, the energy and momentum of the particle will not be the same with things under the black hole's point of view. The book teaches the readers how to calculate them. More than that, the explanation is conceptual and concrete. Reading the part was really enjoyable.Here are some other points.1. When Hawking said "it fills a real gap in the literature for an undergraduate or graduate student course book.", I think that the gap is between freshmen physics textbooks containing special relativity and graduate textbooks like Wald's "General relativity". To read the book, you should know at least the basics in special relativity.2. The book has nearly 600 pages. Most of the readers would not have enough time to read the whole book. The wise readers should choose what to read. There is an appendix entitled Pedagogical Strategy. It was helpful in planning my reading. I recommend the readers to use the appendix also.3. There are some typos in the book. When you get stuck somewhere, it may be because the author is not so skillful in explaining the topic or because there is a typo. Assume the results, just skip, and move forward.4. The variational principle for a free particle (with mass) says that the world line of a free particle between two timelike separated points extremizes the proper time between them. For a photon (that has no mass), we cannot say about proper time. Then, what is the principle for a photon that explains the world line of a photon? You may think that it is ds^2 = 0. But I think this is not enough. For energy and momentum to be conserved, there should be one more principle. Regarding this issue, the book doesn't seem to give the answer.5. The good quality of the papers of the book saved a lot of my eye's fatigue. It doesn't reflect lights. I hope that other textbooks use this kind of papers.

Original Review:I have a math background and got this to learn GR. I couldn't follow the structure though. It tended to go from abstract idea or some experimental result, then give some equation without derivation, and maybe some examples. Some chapters have no equations at all. I really couldn't figure out what it was trying to convey. "Am I just supposed to memorize this, am I supposed to understand it deeply, or is this just thrown in for fun?" Maybe it makes more sense with a lecture to go along with it, but I found it a bit scattered for self-study. Will be looking for something a little more math-forward next time.Update:I tried jumping straight into a more advanced textbook (Wald), and while I could kinda follow it, I felt I was missing some background to really get things, so I came back to this one but with a better understanding of what I needed to get out of it. I saw that chapters 1-6 can be skipped. The real meat begins at chapter 7. (Ch 5 can be useful if you've not been exposed to special relativity). Then I went to Ch 8, skipped a bunch of chapters about applications, then read Ch 20-22. If you really want to get into the meat of GR, this is all you need. The rest is application. This progression follows that of more advanced books like Wald, but with far better concrete examples.

An excellent introduction to general relativity: it's well written, all the ideas are explained at an intuitive level and with an easy-to-understand language; furthermore no mathematical prerequisites of high level are requested.In particular, a first part is a review of special relativity: a not so brief and very good summary, useful to understand the use of the 4-vector notation, too. A successive part is committed to the general relativity foundations (the way which Einstein developed the idea in), the mathematical structure and the analysis of many observations (such as gravitational lensing, cosmic microwave background radiation, universe expansion, etc.) that give confirmations of the theory (with an additional introduction to some cosmological models). A final part is committed to Einstein equation: tensor analysis, curvature, covariant derivative are introduced at this point, and you'll be got up enough to understand all the concepts.Very good binding and hardcover: it's durable and solid, with a good value for money.