The book that educated at least two generations of researchers in gravitational physics. Comprehensive and encyclopedic, the book is written in an often-ideosyncratic style that you will either like or not. A great book at what it does, especially strong on astrophysics, cosmology, and experimental tests. Weinberg is much better than most of us at cranking through impressive calculations. A sensible and lucid introduction to general relativity, with solid coverage of the major topics necessary in a modern GR course. Lightman, W.
Press, R. Price, and S. Advanced General Relativity S. Hawking and G. An advanced book which emphasizes global techniques, differential topology, and singularity theorems; a classic. A mathematical approach, but with an excellent emphasis on physically measurable quantities. Sachs and H. 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.
A short but sweet introduction to some advanced topics, especially spinors, asymptotic structure, and the characteristic initial-value problem. Mathematical Background B. 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.
A rich, readable book on topics in geometry that are of real use to physics, including manifolds, bundles, curvature, Lie groups, and algebraic topology. An accessible introduction to differential geometry and topology, with an emphasis on topics of interest to physicists. The standard text in the field, includes basic topics such as manifolds and tensor fields as well as more advanced subjects. Specialized Topics J. The classic reference for graduate-level electromagnetism.
The problems have left indelible marks on generations of graduate students. Goldstein et al. The classic reference for graduate-level mechanics. An updated edition adds more discussion of nonlinear dynamics. A scary book for some physicists, but an inspiring treatment of classical mechanics from a mathematically sophisticated point of view. A lot of good differential geometry here. Kolb and M. Has become a standard reference for early-universe cosmology, including dark matter, phase transitions, and inflation.
Liddle and D. Focusing on inflation and its implications for large-scale structure, gives a careful treatment of cosmological perturbation theory. A very modern and physical introduction to topics in contemporary cosmology, aimed at advanced undergraduates or beginning graduate students. A graduate-level introduction to cosmology, emphasizing cosmological perturbations, large-scale structure, and the cosmic microwave background. A useful compendium of alternatives to GR and the experimental constraints on them, including a discussion of the parameterized post-Newtonian formalism.
Shapiro and S. A self-contained introduction to the physics and astrophysics of compact stars and black holes. Peskin and D. Has quickly become the standard textbook in quantum field theory.
The standard two-volume introduction to modern string theory, including discussions of D-branes and string duality. A detailed introduction to the extended objects called D-branes which have become an indispensable part of string theory; prior knowledge of string theory itself not required. Falco, P. Schneider, and J. A thorough introduction to the theory and applications of gravitational lensing. Birrell and P. The standard book for people who want a practical introduction to quantum field theory in curved spacetime, including the Hawking effect.
A careful and mathematically rigorous exposition of quantum fields in curved spacetimes; if you really want to know what a vacuum state is, look here. Popular Books K. A truly beautiful exposition of the workings of spacetime. A timely and personal introduction to the physics of string theory. Not afraid to discuss quite advanced concepts, but aiming at a general audience all along; very well written.
A thorough and lucid introduction to all of modern cosmology, focusing on inflation. A nice introduction to supersymmetry, a hypothetical symmetry between bosons and fermions that may be within the reach of particle accelerators soon. Einstein, H. Lorentz, H. Weyl, and H. A scientific biography of Einstein, complete with equations.
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Originally developed for Maple, a Mathematica version is now available. Online Notes and Tutorials See also the Bibliography tab above for actual books. Applications of Classical Physics , Roger Blandford and Kip Thorne An illuminating overview of topics in classical physics by two masters. Advanced undergraduate level; GR is covered briefly at the end. Includes notes, videos of lectures, exercises, and supplemental material. Nominally devoted to high-energy physics, but gradually expanding to keep track of gravitation and astrophysics.
Living Reviews in Relativity Online review articles on all aspects of relativity. Chapter One p. Equations 1. Note that 4. Hartmann, D. Taylor, and J. The irony is that I knew all of this perfectly well, but had somehow convinced myself that there was a more natural atlas for the cone, one that was not smooth. Infrared photons and gravitons - Weinberg, Steven Phys.
Gravitational waves in general relativity. Waves from axisymmetric isolated systems - Bondi, H. A Waves in asymptotically flat space-times - Sachs, R. Symmetries of asymptotically flat 4 dimensional spacetimes at null infinity revisited - Barnich, Glenn et al. BMS charge algebra - Barnich, Glenn et al. The Four laws of black hole mechanics - Bardeen, James M. Black holes and the second law. Nuovo Cimento Lettere 4 Generation of Waves by a Rotating Body - Blandford and R.
Electromagnetic extraction of energy from Kerr black holes - Monthly Notices of the Royal Astron. Black hole equilibrium states. Dewitt and B. Dewitt eds. Evolution of linear gravitational and electromagnetic perturbations inside a Kerr black hole - Ori, Amos Phys. D61 Universality and scaling in gravitational collapse of a massless scalar field - Choptuik, Matthew W. Stability of a Schwarzschild singularity - Regge, Tullio et al.
Stability of the schwarzschild metric - Vishveshwara, C. D1 What happens at the horizon s of an extreme black hole? D80 arXiv D97 no. Disk accretion onto a black hole. Evolution of the hole. Thorne and C. The Science of Interstellar. W Norton. Piran, J. Shaham, and J. D82 arXiv D96 no. B , Phys. B arXiv A standard high-level introduction to Riemannian geometry.
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The inclusion of topics like holonomy and analytic aspects of the theory is appreciated. A somewhat standard introduction to Riemannian and pseudo-Riemannian geometry. Covers a surprising amount of material and is quite accessible. The sections on warped products and causality are very good. Since large parts of the book do not fix the signature of the metric, one can reliably lift many results from O'Neil into GR. A good introduction to general topology and differential topology if you have a strong analysis background. Most, if not all, theorems of general topology used in GR are contained here.
Most of the book is actually algebraic topology, which is not so useful in GR. A standard introduction to differential topology. See Steenrod for details. The first three chapters of this text cover manifolds, lie groups, forms, bundles and connections in great detail, with very few proofs omitted. The rest of the book is on functorial differential geometry, and is seriously advanced.
That material is not needed for GR. A somewhat advanced introduction to differential geometry. Connections in vector bundles are explored in depth. Some advanced topics, like the Cartan-Maurer form and sheaves, are touched upon. Chapter 13, on pseudo-Riemannian geometry, is quite extensive.
A very well-written introduction to general differential geometry that doubles as an encyclopedia for the subject. Most things you need from basic geometry are contained here. Note that connections are not discussed at all. An advanced text on the geometry of connections and Cartan geometries. It provides an alternative viewpoint of Riemannian geometry as the unique modulo an overall constant scale torsion-free Cartan geometry modeled on Euclidean space.
A very rapid and difficult introduction to differential geometry that stresses fiber bundles. Includes an introduction to Riemannian geometry and a lengthy discussion of Chern-Weil theory. A gentle introduction to real analysis in a single variable. This is a good text to "get your feet wet" before jumping into advanced texts like Jost's Postmodern Analysis or Bredon's Topology and Geometry.
Look here for an intuitive yet rigorous the author is Russian explanation of Lagrangian and Hamiltonian mechanics and differential geometry. This book starts from the basics of linear algebra, and manages to cover a lot of basic math used in physics from a physicist's point of view. A handy reference. I recommend you those books from the excellent Chicago Physics Bibliography :. Schutz, B. Schutz's book is a really nice introduction to GR, suitable for undergraduates who've had a bit of linear algebra and are willing to spend some time thinking about the math he develops.
It's a good book for audodidacts, because the development of the theory is pedagogical and the problems are designed to get you used to the basic techniques. Come to think of it, Schutz's book is not a bad place to learn about tensor calculus, which is one of the handiest tools in the physics toolkit. Concludes with a little section on cosmology.
General relativity - Wikipedia
Dirac, P. You might have heard that Paul Dirac was a man of few words. Read this book to find out how terse he could be. It develops the essentials of Lorentzian geometry and of general relativity, up through black holes, gravitational radiation, and the Lagrangian formulation, in a blinding 69 pages! I think this book grew out of some undergrad lectures Dirac delivered on GR; they are more designed to show what the hell theory is all about than to teach you how to do calculations.
I actually didn't like them all that much; they were a little too dry for my taste. It's amusing though, to put Dirac's book next to the book of Misner, Thorne, and Wheeler. D'Inverno, R. I think that D'Inverno is the best of the undergraduate texts on GR an admittedly small group. It's a tad less elementary than Schutz, and it has a lot more detail and excursions into interesting topics.
I seem to remember that it's development of necessary mathematics struck me as somehow lacking, but unfortunately I don't remember what exactly annoyed me. But for physics, I don't think you can beat it. Just be careful: you might find that there's a bit too much here. Misner, C. It's over a thousand pages in length, and probably weighs about 10 pounds. It makes a very effective doorstop, but it would be a shame to use it as one.
I'm not sure I'd recommend it for first time buyers, but after you know a little about the theory, it's about the most detailed, lucid, poetic, humorous, and comprehensive exposition of gravity that you could ask for. MTW is laden with stories and quotations. Oh yes. The theory of general relativity is all laid out in loving detail. You will not find a better explanation of the physics of gravitation anywhere. Well, sorta. MTW is a little out of date. MTW is good for the basics, but there's actually been quite a bit of work done in GR since it's publication in See Wald for details.
Wald, R. My favorite book on relativity. Wald's book is elegant, sophisticated, and highly geometric. That's geometric in the sense of modern differential geometry, not in the sense of lots of pictures, however. If you want pictures, read MTW.
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Fortunately, his exposition is very clear and supplemented by good problems. After he's introduced Einstein's equation, he spends some time on the Schwarzchild and Friedman metrics, and then moves on into a collection of interesting advanced topics such as causal structure and quantum field theory in strong gravitational fields.
Stewart, J. Stewart's book is often for sale at Powell's, which is why I've included it in this list. It's coverage of differential geometry is very modern, and useful if you want some of the flavor of modern geometry. But it's topics are all covered in Wald's book and more clearly to boot. I've been trying to teach myself GTR for about the last twelve months. I find all of the textbooks hard going! I bought Lambourne after spending a lot of time trying to understand Schutz, which is quite rigorous enough for me and a good reference book for my level.
He takes you through the maths quite carefully, but it's not easy and big chunks go straight over my head. I liked it enough to buy a copy though. I bought D'Inverno second hand but I wish I hadn't bothered. Much too difficult, though I do occasionally look at it. Carroll has put a complete course of notes online as well. According to the blurb:. This book is aimed at the enthusiastic general reader who wants to move beyond the maths-lite popularisations in order to tackle the essential mathematics of Einstein's fascinating theories of special and general relativity The reader is then taken gently by the hand and guided through a wide range of fundamental topics, including Newtonian mechanics; the Lorentz transformations; tensor calculus; the Schwarzschild solution; simple black holes and what different observers would see if someone was unfortunate enough to fall into one.
Also covered are the mysteries of dark energy and the cosmological constant; plus relativistic cosmology, including the Friedmann equations and Friedmann-Robertson-Walker cosmological models. To have fun while reading these books, you can enjoy "The Einstein Theory of Relativity: A trip to the fourth dimension", by Lillian Lieber. To me there a two sides to understanding GR.
For the conceptual side you cannot do any better than getting it straight from the horses mouth i. Einstein :. The other side of the coin is the mathematical apparatus. I got a lot of mileage out of this introduction to tensor calculus for GR:. Really focuses on the bare-bones of the math while not omitting the coordinate free treatment.
Only prerequisites are calculus and linear algebra. Then as an additional reference I find L. Landau's text book on theoretical physics Vol 2 very useful. One key title appears missing from the answers provided so far: Einstein Gravity in a Nutshell by Tony Zee. This new book published provides a mathematically rigorous treatment, yet is colloquial in tone and very accessible. The two 'Nutshell titles' combined give an amazingly accessible and complete introductory overview of modern physics. A second recommendation for the A zee book. The other books in the series might be worth your time also.
Zee's stuff is always accessible and insightful, this a wonderful way to get GR into your head, along with some glorious connections to fundamental physics. If you were going to go with a single book, I'd do this one. I'm terrible at math for a physicist so I may have taken a few more books to get my tensors in a row before I could hit the big book. Even at 4th Edition pages it is kind of breathless. The interesting thing about it is the first half is special relativity and electrodynamics which dovetails into the 2nd half which is GR.
One has to persivere because it's terse but not too terse. Like Weinberg it has a more 'physics feel' to than a 'math' one. It is just the basics but done with rigor. Alas , as far as I know,there has been no update since , not sure why. An amusing take on GR is Zel'dovich, Ya. Relativistic Astrophysics, Vol. With a lot of quirky side streets still not treated in other books , alas also not updated since Russian books that seem to be just about Black Holes usually have a good introduction to GR, and are kind of quirky to my amusement with their diversions! If you want real 'brain burn Chandrasekhar's The Mathematical Theory of Black Holes is totally comprehensive, if exhausting ,another book like MTW for one's shelf as a reference.
It all depends on your background. Still, it is rigorous it even says so in the title! They don't go very far, but do touch upon some solutions e. Schwarzschild and cosmology. Its the only textbook I have managed to find which really explains things so I can understand each line and also covers the main advanced aspects of the theory. I would also definitely suggest you should have read a good book on special relativity before tackling MTW.
This answer contains some additional resources that may be useful. Please note that answers which simply list resources but provide no details are strongly discouraged by the site's policy on resource recommendation questions. This answer is left here to contain additional links that do not yet have commentary. You can't beat a bit of Hobson. Most of the resources I could recommend have already been listed here, but one source that I cannot recommend enough is the collection of video lectures from the master's program at Perimeter Institute for Theoretical Physics:.
The General Relativity lectures are mostly unchanged from year to year, as well as the Gravitational Physics lectures, but it is nice that there are many years to choose from. Neil Toruk's wonderful lectures are under "Relativity" the "core" tab of every year, which provide a nice basis for study into GR.
Spacetime and Geometry
A more rigorous approach including work into Hawking radiation, boundary terms, cosmic strings, and the Cartan formalism is covered in Ruth Gregory's excellent lectures. They are found under "Gravitational Physics" in the "review" tab of any year. I am always amazed how few people know that these lectures exist.