Solutions Manual Wald General Relativity
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Lecture Notes on General Relativity - S. Carroll Bibliography The typical level of difficulty (especially mathematical) of the books is indicated by a number of asterisks, one meaning mostly introductory and three being advanced. The asterisks are normalized to these lecture notes, which would be given.
The first four books were frequently consulted in the preparation of these notes, the next seven are other relativity texts which I have found to be useful, and the last four are mathematical background references. Schutz, A First Course in General Relativity (Cambridge, 1985).
- A First Course in General Relativity Bernard F Schutz (2nd Edition, Cambridge University Press, 2009) Solutions to Selected Exercises (Version 1.0, November 2009) To the user of these solutions.
- General Relativity Wald Solutions Manual General relativity (springer undergraduate mathematics, buy general relativity (springer undergraduate mathematics series) on amazoncom free shipping on qualified orders. Problem book in relativity and gravitation: alan p, buy problem.
This is a very nice introductory text. Especially useful if, for example, you aren't quite clear on what the energy-momentum tensor really means. Weinberg, Gravitation and Cosmology (Wiley, 1972). A really good book at what it does, especially strong on astrophysics, cosmology, and experimental tests. However, it takes an unusual non-geometric approach to the material, and doesn't discuss black holes.
Thorne and J. Wheeler, Gravitation (Freeman, 1973). A heavy book, in various senses. Most things you want to know are in here, although you might have to work hard to get to them (perhaps learning something unexpected in the process). Wald, General Relativity (Chicago, 1984).
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Thorough discussions of a number of advanced topics, including black holes, global structure, and spinors. The approach is more mathematically demanding than the previous books, and the basics are covered pretty quickly. Taylor and J. Wheeler, Spacetime Physics (Freeman, 1992). A good introduction to special relativity. D'Inverno, Introducing Einstein's Relativity (Oxford, 1992). A book I haven't looked at very carefully, but it seems as if all the right topics are covered without noticeable ideological distortion.
Lightman, W.H. Price, and S.A.
Teukolsky, Problem Book in Relativity and Gravitation (Princeton, 1975). A sizeable collection of problems in all areas of GR, with fully worked solutions, making it all the more difficult for instructors to invent problems the students can't easily find the answers to. Straumann, General Relativity and Relativistic Astrophysics (Springer-Verlag, 1984). A fairly high-level book, which starts out with a good deal of abstract geometry and goes on to detailed discussions of stellar structure and other astrophysical topics. De Felice and C. Clarke, Relativity on Curved Manifolds (Cambridge, 1990). A mathematical approach, but with an excellent emphasis on physically measurable quantities.
Hawking and G. Ellis, The Large-Scale Structure of Space-Time (Cambridge, 1973). An advanced book which emphasizes global techniques and singularity theorems. Wu, General Relativity for Mathematicians (Springer-Verlag, 1977).
Just what the title says, although the typically dry mathematics prose style is here enlivened by frequent opinionated asides about both physics and mathematics (and the state of the world). Schutz, Geometrical Methods of Mathematical Physics (Cambridge, 1980). Another good book by Schutz, this one covering some mathematical points that are left out of the GR book (but at a very accessible level).
Included are discussions of Lie derivatives, differential forms, and applications to physics other than GR. Guillemin and A.
Pollack, Differential Topology (Prentice-Hall, 1974). An entertaining survey of manifolds, topology, differential forms, and integration theory. Sen, Topology and Geometry for Physicists (Academic Press, 1983). Includes homotopy, homology, fiber bundles and Morse theory, with applications to physics; somewhat concise. Warner, Foundations of Differentiable Manifolds and Lie Groups (Springer-Verlag, 1983). The standard text in the field, includes basic topics such as manifolds and tensor fields as well as more advanced subjects.
This is a classic text, but 'classic' isn't completely a good thing. General relativity is a living field, and 29 years is a long time. The book never had an acceptable amount of contact with observation, and that shortcoming has become even more severe with the passage of time; it predates LIGO, Gravity Probe B, modern studies of CMB anisotropy, and the discoveries of supermassive black holes and the nonzero cosmological constant. Pedagogically, I would not recommend this book for someone encountering GR for the first time. For a first-time student, a more appropriate text would be Carroll or the also-classic Misner, Thorne, and Wheeler.
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For someone who is serious about GR, the book is useful because it treats some advanced topics in a more accessible fashion than one can find elsewhere. For a first-time student, a more appropriate text would be Carroll or the also-classic Misner, Thorne, and Wheeler. For someone who is serious about GR, the book is useful because it treats some advanced topics in a more accessible fashion than one can find elsewhere.For a very first look at GR without already having a background in differential geometry, I think a quick read the first few chapters of Schutz is a good idea.
After that, I second the recommendation for Carroll (and I think it would be wise to read before MTW). Of course, Carroll (and most others) don't assume prior knowledge of differential geometry either, but Schutz takes you through it at such a leisurely pace that it's especially good for first exposure. I usually suggest the Schutz Carroll sequence for introductions, followed by either Wald or MTW for further study. I wouldn't recommend Schutz over Carroll at all. Schutz butchers the beautiful subject of differential geometry and if you've seen in the past on people asking specific questions from the text on this forum, it is usually tied to his horrible exposition of differential geometry. As a golden rule of thumb: never learn a math subject from a physics textbook especially when the subject forms the very core of the underlying physical theory. Wald is top notch - nothing bad to say about it at all and Carroll is also good (less advanced but still covers a lot and his tone is very gentle).
Wald is very mathematical which, for me anyways, makes it much more enjoyable. Carroll sometimes handwaves the mathematics but he still explains everything at a nice level of rigor. I think Wald is fine as a first book on GR, but I would only recommend it (as a first book) to a very serious student who's studying differential geometry at the same time. I recommend the books by John M.
Lee for that, 'Introduction to smooth manifolds' and 'Riemannian manifolds: an introduction to curvature'. These books are excellent. The only problem is that you need both of them. I also second the recommendation to read the first few chapters of Schutz first.
Wald only devotes one page to SR, but Schutz covers it very thoroughly. Schutz also contains a nice introduction to tensors. (Edit: Just to make it perfectly clear, the following two sentences are about Schutz, not Wald).
It's a GR book, but what makes it good are the parts about SR and tensors. The part about GR is too thin on differential geometry for my taste. To those of you who've read/worked with all of the big name GR texts (Wald, MTW, Weinberg, Landau's fields), if you were to buy only one of them which one would you pick? I'm looking for an encyclopedic thing that will keep me coming back but I would like it to have some treatment on gravitational waves. I've taken a 'mathematical methods for GR' course so I wouldn't be spending much time on the first few chapters(but it would be nice if it were self-contained like Landau's classical theory of fields). I've read some of Carroll's but I really didn't like it(too many handwavy explanations, it just doesn't flow well), and a bit of Weinberg's 'Gravitation and Cosmology' and I really liked it(notation was identical to my course), but I only read the intro chapters on tensor calculus and not the actual physics. That's kind of what I was trying to avoid, as my course pretty much consisted of exercises like this (mostly simpler things, ie tensor transformation of Christoffel symbols,general tensor identity proofs, grinding out Ricci components and curves from a given metric but no actual derivation of the Schwarschild or FLRW metrics.)If you look at chapter 11 of Wald, problem 11.6 is a funny one because the first two parts of the problem are insanely trivial whereas the third part asks you to calculate the Komar integral for the total angular momentum of the charged kerr space-time.
It was such a painful calculation that I cried, several times. EDIT: Just to clarify, Wald does derive the main results (e.g. Schwarzschild metric) and uses very satisfying geometric arguments in doing so. Also, just for fun, here is a worked out example of another typical tensor calculus problem from Wald (problem 7.1, so yeah same chapter as the one I mentioned above lol). Wald has almost no applications and makes almost no connection with experiment, which makes it a poor choice for a student's first introduction to GR. I would start with Taylor and Wheeler's Spacetime Physics, which, although it's an SR text, actually has quite a bit of material in it that explicitly prepares you for GR.
Pervect's suggestion of reading an undergrad GR text is also excellent. Hartle is good. Exploring Black Holes is a fine book as far as it goes, but its focus is very narrow, and it won't prepare you with any of the mathematical techniques. Rather than Wald, which is extremely out of date, I would suggest Carroll. There is even a free preliminary version of Carroll online.