Books for general relativity

Question

What are some good books for learning general relativity?

Answer 1

I can only recommend textbooks because that's what I've used, but here are some suggestions:

• Gravity: An Introduction To General Relativity by James Hartle is reasonably good as an introduction, although in order to make the content accessible, he does skip over a lot of mathematical detail. For your purposes, you might consider reading the first few chapters just to get the "big picture" if you find other books to be a bit too much at first.
• A First Course in General Relativity by Bernard Schutz is one that I've heard similar things about, but I haven't read it myself.
• Spacetime and Geometry: An Introduction to General Relativity by Sean Carroll is one that I've used a bit, and which goes into a slightly higher level of mathematical detail than Hartle. It introduces the basics of differential geometry and uses them to discuss the formulation of tensors, connections, and the metric (and then of course it goes on into the theory itself and applications). It's based on these notes which are available for free.
• General Relativity by Robert M. Wald is a classic, though I'm a little embarrassed to admit that I haven't read much of it. From what I know, though, there's certainly no shortage of mathematical detail, and it derives/explains certain principles in different ways from other books, so it can either be a good reference on its own (if you're up for the detail) or a good companion to whatever else you're reading. However it was published back in 1984 and thus doesn't cover a lot of recent developments, e.g. the accelerating expansion of the universe, cosmic censorship, various results in semiclassical gravity and numerical relativity, and so on.
• Gravitation by Charles Misner, Kip Thorne, and John Wheeler, is pretty much the authoritative reference on general relativity (to the extent that one exists). It discusses many aspects and applications of the theory in far more mathematical and logical detail than any other book I've seen. (Consequently, it's very thick.) I would recommend having a copy of this around as a reference to go to about specific topics, when you have questions about the explanations in other books, but it's not the kind of thing you'd sit down and read large chunks of at once. It's also worth noting that this dates back to 1973, so it's out of date in the same ways as Wald's book (and more).
• Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity by Steven Weinberg is another one that I've read a bit of. Honestly I find it a bit hard to follow - just like some of Weinberg's other books, actually - since he gets into such detailed explanations, and it's easy to get bogged down in trying to understand the details and forget about the main point of the argument. Still, this might be another one to go to if you're wondering about the details omitted by other books. This is not as comprehensive as the Misner/Thorne/Wheeler book, though.
• A Relativist's Toolkit: The Mathematics of Black-Hole Mechanics by Eric Poisson is a bit beyond the purely introductory level, but it does provide practical guidance on doing certain calculations which is missing from a lot of other books.

Answer 2

This list is extensive, but not exhaustive. I am aware that there are more standard GR books out there such as Hartle and Schutz, but I don’t think these are worth mentioning. Books with stars are, in my opinion, “must have” books. (I) denotes introductory, (IA) denotes advanced introductory, i.e. the text is self-contained but it would be very helpful to have experience with the subject and (A) denotes advanced.

Special Relativity

• E. Gourgoulhon (2013), Special Relativity in General Frames. (A) $\star$

This is a rigorous and encyclopedic treatment of special relativity. It contains pretty much everything you will ever need in special relativity, like the Lorentz factor for a rotating, accelerating observer. It is not an introduction, the author does not bother to motivate the Minkowski metric structure at all.

Introductory General Relativity

These books are "introductory" because they assume no knowledge of relativity, special or general. Additionally, they do not require the reader to have any knowledge of topology or geometry.

• S. Carroll (2004), Spacetime and Geometry. (I) $\star$

A standard first book in GR. There isn't much to say here, it's an excellent, accessible text that gently introduces differential and Riemannian geometry.

• A. Zee (2013), Einstein Gravity in a Nutshell. (I) $\star$

This is one of the best physics books ever written. This can be comfortably read by anyone who knows $F=ma$, vector calculus and some linear algebra. Zee even completely develops the Lagrangian formalism from scratch. The math is not rigorous, Zee focuses on intuition. If you can't handle a book talking about Riemannian geometry without the tangent bundle, or even charts, this isn't for you. It's rather large, but manages to go from $F=ma$ to Kaluza-Klein and Randall-Sundrum by the end. Zee frequently comments on the history or philosophy of physics, and his comments are always welcome. The only weakness is that the coverage of gravitational waves is simply bad. Other than that, simply fantastic. (Less advanced than Carroll.)

Advanced General Relativity

These books either require previous knowledge of relativity or geometry/topology.

• Y. Choquet-Bruhat (2009), General Relativity and the Einstein Equations. (A)

A standard reference for the Cauchy problem in GR, written by the mathematician who first proved it is well-posed.

-S.W. Hawking and G.F.R. Ellis (1973), The Large Scale Structure of Space-Time. (A) $\star$

The classic book on spacetime topology and structure. The chapter on geometry is really meant as a reference, not everything is given a proper proof. They present GR axiomatically, this is not the place to learn the basics of the theory. This text greatly expands upon chapters 8 through 12 in Wald, and Wald constantly references this in those chapters. Hence, read after Wald. For mathematicians interested in general relativity, this is a major resource.

• P. Joshi (2012), Gravitational Collapse and Spacetime Singularities. (A)

A modern discussion of gravitational collapse for physicists. (That is, it's not a hardcore mathematical physics monograph, but also not handwave city.)

• M. Kriele (1999), Spacetime. (IA)

While technically an introduction, because the reader need not know anything about relativity to read this, it's quite mathematically sophisticated.

• R. Penrose (1972), Techniques of Differential Topology in Relativity. (A)

This is a proof graveyard. Some of the proofs here are not found anywhere else. If you're willing to skip 70 pages of pure math and take the results on faith, skip this. It overlaps with Hawking & Ellis a lot.

• E. Poisson (2007), A Relativist’s Toolkit. (A) $\star$

This is really a toolkit, you're assumed to know basic GR coming in, but will leave with an idea of how to do some of the more complicated computations in GR. Includes a very good introduction to the Hamiltonian formalism in GR (ADM).

• R.K. Sachs and H. Wu (1977), General Relativity for Mathematicians. (A)

This is an extremely rigorous text on GR for mathematicians. If you don't know what "let $M$ be a paracompact Hausdorff manifold" means, this isn't for you. They do not explain geometry (Riemannian or otherwise) or topology for you. Put aside the strange notation and (sometimes stupid) comments on physics vs. mathematics and you have a solid text on the mathematical foundations of GR. It would be most helpful to learn GR from a physicist before reading this.

• J. Stewart (1991), Advanced General Relativity. (A)

A standard reference for spinor analysis in GR, the Cauchy problem in GR, and Bondi mass.

• N. Straumann (2013), General Relativity. (IA) $\star$

A mathematically sophisticated text, thought not as much as Sachs & Wu. The coverage of differential geometry is rather encyclopedic, it's hard to learn it for the first time from here. If you're a mathematician looking for a first GR book, this could be it. Besides the overall "mathematical" presentation, notable features are a discussion of the Lovelock theorem, gravitational lensing, compact objects, post-Newtonian methods, Israel's theorem, derivation of the Kerr metric, black hole thermodynamics and a proof of the positive mass theorem.

• R.M. Wald (1984), General Relativity. (IA) $\star$

The standard graduate level introduction to general relativity. Personally, I'm not a fan of the first four chapters, the reader is much better off reading Wald with a basic understanding of GR and geometry. However, the rest of the text is excellent. If you can only read one text in the "advanced" list, it should be Wald. Some topology would be good, the appendix on it is not very extensive.

General Relativity Reference Texts

These are some canonical reference texts.

• S. Chandrasekhar (1983), The Mathematical Theory of Black Holes. (A)

Pages and pages of calculations. More pages of calculations. This book has derivations of all black hole solutions, geodesic trajectories, perturbations, and more. Not something you would sit down and read for fun.

• C.W. Misner, K.S. Thorne, and J.A. Wheeler (1973), Gravitation. (I)

The most cited text in the field. It is absolutely massive and covers so much. Be warned, it's somewhat out-of-date and the notation is generally terrible. The best use for MTW is to look up a result every now and then, there are better books to learn from.

• H. Stephani, et al. (2009), Exact Solutions of Einstein’s Field Equations. (A)

If an exact solution of the Einstein equations was found before 2009, it is in this book and is likely accompanied by a derivation, a sketch of the derivation and some references.

• S. Weinberg (1972), Gravitation and Cosmology. (I)

Weinberg takes an interesting philosophical approach to GR in this book, and it's not good for an introduction. It was the standard reference for cosmology in the 70s and 80s, and it's not unheard of to reference Weinberg in 2016.

Riemannian and Pseudo-Riemannian Geometry

Texts focused entirely on the geometry of Riemannian and Pseudo-Riemannian manifolds. These all require knowledge of differential geometry beforehand, save for O'Neil.

• J.K. Beem, P.E. Ehrlich, and K.L. Easley (1996), Global Lorentzian Geometry. (A)

A very advanced text on the mathematics of Lorentzian geometry. The reader is assumed to be familiar with Riemannian geometry. Hawking & Ellis, Penrose and O'Neil are crucial, this book builds on the material in those texts (and the authors tend to not repeat proofs that can be found in those three). The sprit of the book is to see how many results from Riemannian geometry have Lorentzian analogues. The actual applications to physics are speculative.

• J. Cheeger and D.G. Ebin (1975), Comparison Theorems in Riemannian Geometry. (A)

An advanced text on Riemannian geometry, the authors explore the connection between Riemannian geometry and (algebraic) topology. Many of the concepts and proofs here are used again in Beem and Ehrlich.

• M.P. do Carmo (1992), Riemannian Geometry. (I) $\star$

A terrific introduction to Riemannian geometry. The presentation is leisurely, it's a joy to read. Notable topics covered are global theorems like the sphere theorem.

• J.M. Lee (1997), Introduction to Riemannian Manifolds. (I)

A standard introduction to Riemannian geometry. When I don't understand a proof in do Carmo or Jost, I look here. It covers somewhat less material than do Carmo, though they are similar in spirit.

• J. Jost (2011), Riemannian Geometry and Geometric Analysis. (IA)

An advanced "introduction" to Riemannian geometry that covers PDE methods (for instance, the existence of geodesics on compact manifolds is proved using the heat equation), Hodge theory, vector bundles and connections, Kähler manifolds, spin bundles, Morse theory, Floer homology, and more.

• P. Petersen (2016), Riemannian Geometry. (IA)

A standard high-level introduction to Riemannian geometry. The inclusion of topics like holonomy and analytic aspects of the theory is appreciated.

• B. O’Neil (1983), Semi-Riemannian Geometry with Applications to Relativity. (I) $\star$

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.

Topology

Texts that will elucidate the topological aspects of GR and geometry.

• G.E. Bredon (1993), Topology and Geometry. (IA) $\star$

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.

• V. Guillemin and A. Pollack (1974), Differential Topology. (I)

A standard introduction to differential topology. Some results useful for GR include the Poincare-Hopf theorem and the Jordan-Brouwer theorem.

• J. Milnor (1963), Morse Theory.

The classical introduction to Morse theory, which is used explicitly in Beem, Ehrlich & Easley and Cheeger & Ebin and implicitly and Hawking & Ellis and others.

• N.E. Steenrod (1951), The Topology of Fiber Bundles.

Most advanced GR books contain the following: "The manifold $M$ admits a Lorentzian metric if and only if (a) $M$ is noncompact, (b) $M$ is compact and $\chi (M)=0$. See Steenrod (1951) for details." This book contains the most fundamental topological theorem of GR, that, to my knowledge, is not proved anywhere else.

Differential Geometry

Texts on general differential geometry.

• S. Kobayashi and K. Nomizu (1963), Foundations of Differential Geometry (Vol. 1, 2). (A)

This is the standard reference for connections on principal and vector bundles.

• I. Kolar, P.W. Michor, and J. Slovak (1993), Natural Operations in Differential Geometry. (A)

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.

• J.M. Lee (2009), Manifolds and Differential Geometry. (IA)

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.

• J.M. Lee (2013), Introduction to Smooth Manifolds. (I) $\star$

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.

• R.W. Sharpe (1997), Differential Geometry. (A)

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.

• G. Walschap (2004), Metric Structures in Differential Geometry. (IA)

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.

Misc.

• S. Abbot (2015), Understanding Analysis. (I)

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.

• V.I. Arnold (1989), Mathematical Methods of Classical Mechanics. (IA) $\star$

Look here for an intuitive yet rigorous (the author is Russian) explanation of Lagrangian and Hamiltonian mechanics and differential geometry.

• K. Cahill (2013), Physical Mathematics. (I)

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.

• L.C. Evans (2010), Partial Differential Equations.

The standard graduate level introduction to partial differential equations.

• J. Jost (2005), Postmodern Analysis. (A)

An advanced analysis text which goes from single-variable calculus to Lebesgue integration, $L^p$ spaces and Sobolev spaces. Contains proofs of theorems such as Picard-Lindelöf, implicit/inverse function and Sobolev embedding, which are ubiquitous in geometry and geometric analysis.

Answer 3

I recommend you those books from the excellent Chicago Physics Bibliography:

• Schutz, B., A First Course in Generaly Relativity

  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.

• Dirac, P.A.M., General Relativity

  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., Introducing Einstein's Relativity

  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., Thorne, K., & Wheeler, J.A., Gravitation

  Gravitation has a lot of nicknames: MTW, the Phonebook, the Bible, the Big Black Book, etc,... 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. MTW was written in the late 60's/early 70's by three of the best gravitational physicists around--Kip Thorne, Charles Misner, and John Wheeler--and it's a truly great book. 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. Poetic? Humorous? Yep. MTW is laden with stories and quotations. Detailed? Lucid? 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. Comprehensive? 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 1973. See Wald for details.

• Wald, R., General Relativity

  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.) After a concise introduction to the theory of metric connections & curvature on Lorentzian manifolds, Wald develops the theory very quickly. 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., Advanced General Relativity

  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.

Answer 4

I've been trying to teach myself GTR for about the last twelve months. I stopped my formal maths/physics education when I was 18, many years ago.

IMveryveryHO you could do worse than starting with the twelve video lectures by Leonard Susskind of Stanford University. They're on YouTube but there's a general link here http://www.cosmolearning.com/courses/modern-physics-general-relativity/ They really are excellent.

I find all of the textbooks hard going! But I liked Lambourne (Relativity, Gravitation and Cosmology) - about the most accessible of the bunch, I found. 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 also like Foster and Nightingale which is nice and concise and which I got cheap second hand.

I bought D'Inverno second hand but I wish I hadn't bothered. Much too difficult, though I do occasionally look at it.

I tried Relativity Demystified but it didn't.

Carroll has put a complete course of notes online as well. See http://ned.ipac.caltech.edu/level5/March01/Carroll3/Carroll_contents.html

You might also want to take a look at A Most Incomprehensible Thing: Notes Towards a Very Gentle Introduction to the Mathematics of Relativity by Collier. 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 first chapter provides a crash course in foundation mathematics. 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.

Answer 5

I think D'Inverno's "Introducing Einstein's Relativity" is a good text for a rigorous primer in GR.

The following link could be useful for you:

http://www.desy.de/user/projects/Physics/Administrivia/rel_booklist.html

To have fun while reading these books, you can enjoy "The Einstein Theory of Relativity: A trip to the fourth dimension", by Lillian Lieber.

Answer 6

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.e. Einstein):

http://www.bartleby.com/173/

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:

http://web.mit.edu/edbert/GR/gr1.pdf

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. D. Landau's text book on theoretical physics Vol 2 very useful.

Answer 7

One key title appears missing from the answers provided so far: Einstein Gravity in a Nutshell by Tony Zee. This new book (published 2013) provides a mathematically rigorous treatment, yet is colloquial in tone and very accessible. I own Wald, Schutz, and Hartle, but Zee's book has quickly developed into my favorite text on General Relativity.

Those who have read Zee's Quantum Field Theory in a Nutshell know what to expect. The two 'Nutshell titles' combined give an amazingly accessible and complete introductory overview of modern physics.

Answer 8

I learned my GR from Landau and Lifshitz Classical Theory of Fields, 2nd edition. Even at 402 (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 1974, not sure why. An amusing take on GR is Zel'dovich, Ya. B. and Novikov, I. D. Relativistic Astrophysics, Vol. 1: Stars and Relativity.

With a lot of quirky side streets still not treated in other books , alas also not updated since 1971... tho Frolov and Novikov's 1998 Black Hole Physics: Basic Concepts and New Developments is kind of a sequel with more GR off shoots.

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.

Answer 9

A second recommendation for the A zee book. I'd say GRAVITATION is the goal,but I'd get there by:

"Exploring Blackholes" by Wheeler, nice intro, stops at Schwartzchild.

then the soft introduction provided by piccioni, which exists in many places (amazon, nook, oyster) but not in print, oddly. "General Relativity" 1-3. The other books in the series might be worth your time also.

"Einstein Gravity in a nutshell" A. Zee. 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.

From here, maybe, possibly, you can start and finish the glory that is GRAVITATION. 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.

While we're here, "A general relativity workbook" is an excellent resource.

See also: http://www.desy.de/user/projects/Physics/Administrivia/rel_booklist.html http://math.ucr.edu/home/baez/physics/Administrivia/rel_booklist.html#intro_gr

Answer 10

I'm a bit late to the party here, but I believe I have something to contribute.

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:

https://www.perimeterinstitute.ca/training/perimeter-scholars-international/psi-lectures

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.

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. They cover everything that a beginning graduate student in theoretical physics would need to know. I cannot speak highly enough of them. The Perimeter Institute has truly given a gem that more people should know about.

I hope this helps!

Answer 11

I'm surprised I haven't seen Relativity: Special, General, and Cosmological by Wolfgang Rindler suggested yet. I'm self-studying relativity and have tried starting quite a few of the books mentioned earlier. What sets this book apart is its emphasis on the physics of relativity as well as the mathematics. Concepts that in a lot of other introductory textbooks are taken for granted are here carefully motivated (a good example is Rindler's discussion on why exactly we should model spacetime as a 4-dimensional pseudo-Riemannian manifold with Minkowskian signature).

Answer 12

It all depends on your background. The recent translation to English of Grøn/Næss Norwegian GR book is a very easy and plesant read:

Einstein's Theory: A Rigorous Introduction for the Mathematically Untrained

Still, it is rigorous (it even says so in the title!). They don't go very far, but do touch upon some solutions (e.g. Schwarzschild) and cosmology.

Answer 13

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.

• Lillian Lieber: Einstein's Theory of Relativity.

• You can't beat a bit of Hobson.

• The lecture notes by Geroch. Including notes on general relativity.

Answer 14

There are already a lot of answers that lists all the well-known books of General Relativity. But it is not possible to learn a subject by reading hundreds of books. So I wouldn't give a long list, rather I will try to discuss which books to read and the reason to choose that book.

The advanced level texts are marked with ($^*$) and the texts suitable for conceptual knowledge are marked with ($^\dagger$).

• The Classical Theory of Fields (Landau and Lifshitz)$^\dagger$

This is undoubtedly a classic text written by Landau, a giant of twentieth-century theoretical physics and an original thinker. The general relativity portion is not much detailed, but it gives the reader an impression of the Landau-way of thinking. The explanations are concise but elegant. It is suitable for beginners and learning from Landau's text has its own benefits, particularly for those interested in research.

• Feynman Lectures on Gravitation (Feynman)$^\dagger$

This text is based on a course that Feynman gave at Caltech during the academic year 1962-63. Feynman took an untraditional non-geometric approach to general relativity based on the underlying quantum aspects of gravity. However, these lectures represent a useful record of his viewpoints and his physical insights into gravity and its applications. Though it is not suitable as a textbook, it contains some of the crucial concepts of the subject which are not found elsewhere. Above all, one could visualize the Feynman-way of thinking general relativity.

• Gravity: An Introduction to Einstein's General Relativity (Hartle)

A text suitable for undergraduates, particularly those who step first in general relativity. It starts with all sorts of explanations based on Newtonian concepts before discussing the field equations. However, tensors and geometrical ideas are only introduced at the end.

• Gravitation: Foundation and Frontiers (Padmanabhan)$^\dagger$

As the title suggests, the text is divided into two parts. The 'Foundation' portion includes basic ideas of special and general relativity whereas the 'Frontiers' portion includes advanced topics like QFT in curved spacetime, gravity in higher dimensions, emergent gravity etc. This well written text follows a nice pedagogy and suitable for a basic as well as advanced course. There are also some excellent discussions of conceptual ideas not found elsewhere. Added to all, there is a rich collection of problems that are aimed to fill the gap between textbook study and research.

• General Relativity (Wald)

Wald's text is a classic and undoubtedly one of the most familiar text in general relativity.It is concise, lucid as well as mathematically rigorous. It starts with basic concepts of differential geometry and then explains general relativity using the geometric viewpoint. It also includes several advanced topics like spinors, quantum fields in curved spacetime etc. However, this might not be suitable for undergraduate students in Physics who hadn't done a course on differential geometry.

• A First Course in General Relativity (Schutz)

This one is really a nice place to learn general relativity. This text also start by introducing differential geometry, however the explanations are more extensive as compared to Wald. It is also a nice place to learn tensor calculus where one can find excellent discussions on geometric nature of tensors.

• The Large Scale Structure of Spacetime (Hawking and Ellis)$^*$

This is an advanced level text and a classic that is not suitable for the faint hearted. This concise text uses rigorous differential geometric viewpoint to explain general relativity. The subject is not dealt at great depth, but the explanations of the mathematical background is complete and original. Undoubtedly this is a gem and a must read for those who are interested in the mathematical details of general relativity.

• Gravitation (Misner, Thorne and Wheeler)$^*$

MTW, The Bible, The Big Black Book or whatever you may call, this one is not really a textbook. This is one of the most detailed, comprehensive and complete text ever written in general relativity. This is a must-have reference that everyone working on general relativity should have with him. It is said that if you have any doubt in the subject, then the answer should be available in MTW.

• Introducing Einstein's Relativity (d'Inverno)

This text is concise and clearly written and suitable for undergraduates. It features a well-balanced but self-contained selection of topics that follows nice pedagogy and moreover it is full of physical insight. A great deal of illustrations are included that makes the presentation excellent and well-readable.

• The Mathematical Theory of Black Holes (Chandrasekhar)$^*$

This is a classic and authoritative text in the subject of black holes that have pages and pages of calculations. This monograph is mathematically too rigorous and not suitable for the faint hearted. This text contains the most extensive discussion of black holes. However, the reader needs to master the tetrad and Newman-Penrose formalism which is rigorously used in the text. In single word, this one is a masterpiece.

• Relativity, Thermodynamics and Cosmology (Tolman)$^\dagger$

Though outdated, this is a classic text in the field of general relativity. Written in a logical and comprehensive manner, special and general relativity is discussed in finer details, including their extensions to all the important domains in macroscopic physics. Physical point of view is used throughout the text rather than mathematical point of view which helped to emphasize the physical nature of assumptions and conclusions rather than mathematical rigor. This is one of the best text that features conceptual explanations of the subject.

Answer 15

Adding two more in the list...

• Gravitation: Foundations and Frontiers by T. Padmanabhan
• An Introduction to General Relativity and Cosmology by J. Plebanski and A. Krasinski

These are 'mathematically rigorous' with lots of exercises and projects with hints to many of them. In my opinion these may be a good start for GR and its applications.

Answer 16

I would suggest it really is worth reading Misner, Thorne, and Wheeler (MTW). 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.

Answer 17

The book by Ta-Pei Cheng "Relativity, Gravitation and Cosmology: A Basic Introduction" is maybe the best book I have read on the subject.
It is also recommended by Gerard t'Hooft here:
https://www.staff.science.uu.nl/~gadda001/goodtheorist/texts&resources.html

Also, as some other stated, Zee's book "Gravity in a Nutshell" is pretty great too!

Answer 18

An excellent concise and readable book (although a bit old) :
H. Yilmaz, Introduction to the Theory of Relativity and the Principlies of Modern Physics, Blaisdell Publishing, 1964.

Answer 19

To get a first idea of what GR is all about, with loads of solved exercises, try General Relativity Without Calculus.

Answer 20

I am adding an answer which is written from my perspective of having learned the subject mainly from textbooks, and for teaching undergraduates. The following list is focused on books suitable for undergraduates. It is in alphabetical order, then I give my own opinion on recommendations at the end.

-- S. Carroll, Spacetime and Geometry, Pearson

A good book but a bit terse for the beginner. What I mean is, Carroll is eager to get to some more advanced topics but this means he is a bit too quick, in my opinion, on introducing some differential geometry ideas which you don't need in order get started, and as a result he doesn't have time to show the beginner how you really solve basic problems such as Schwarzschild metric, orbits and the like. However when I needed some of the slightly more advanced ideas, this was a very clear place to find them.

-- B. Crowell, General Relativity, www.lightandmatter.com

Helpful, free, correct level for learning. But not the main resource I think.

-- R. D'Inverno, Introducing Einstein's Relativity, Clarendon Press

Intended to be introductory by I found it impenetrable until I had learned the subject by other means.

-- P. A. M. Dirac, General Theory of Relativity, Princeton University Press

A good back-up reference getting straight down to business, showing helpfully direct derivations. But not as much explanation as a first learner would want.

-- M. P. Hobson, G. Efstathiou and A. N. Lasenby, General relativity, An introduction for physicists, Cambridge University Press

The most helpful introduction I found. Good level, clear explanation, gets the balance right of how many mathematical tools to introduce. Aimed at the physicist who wants to find out how to use the theory in astronomy, not just conjure weird manifolds. Perhaps mathematicians would want more differential geometry.

-- Lightman, Press, Price and Teukolsky, Problem book in relativity and gravitation, Princeton University Press.

Out of print I think but a useful collection of specific problems and specific answers, showing you how you actually do G.R. rather than just the high-level stuff. Very useful.

-- C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation, W. H. Freeman and Co.

The classic tome. You should consult it by dipping in for each subject, but I would not recommend it as the main text by which to learn for a beginner.

-- E. Poisson, A Relativist's Toolkit, Cambridge University Press

Useful as a back-up resource.

-- W. Rindler, Relativity: Special, General and Cosmological, Oxford University Press

Good for learning but I prefer a less terse way in.

-- B. Schutz, A First Course in General Relativity, Cambridge University Press

Same level as Hobson, Efstathiou and Lasenby, very suitable as a way in.

-- A. Steane, Relativity made relatively easy volume 2: General relativity and cosmology, Oxford University Press

I wrote this book so I have an interest, but it would not be appropriate to leave it out. This book is intended as a way in for undergraduates. It is thorough on how you do the maths, showing many of the details which are glossed over in more advanced texts. It is also much more thorough on cosmology than is common for introductory books on G.R. Finally, it has plenty of physical explanation aimed at providing intuition.

-- R. Wald, General Relativity, University of Chicago Press.

This is a classic reference and great for graduate level, once you have got started using some less advanced text.

Now for my own recommendation. For an undergraduate I would recommend my own book first, because I wrote (like any author) the book I would have wanted to read. My order of recommendation, for someone learning at undergraduate level, and with the physicist's yearning for physical understanding alongside mathematical method, is:

1. Steane
2. Hobson, Efstathiou and Lasenby
3. Schutz
4. Carroll
5. Various others to be used as resources, such as MTW, Rindler, Lightman et al

Answer 21

Spacetime Physics by Taylor/Wheeler

(a red book, with white text on it)

and this book as well

General Relativity, Black Holes, and Cosmology by Andrew J. S. Hamilton 4 December 2021 Available here (free)

• https://jila.colorado.edu/%7Eajsh/courses/astr5770_21/text.html

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footnotes

my view on it | Really a great introductory book, has references, examples, analogies, and is funny especially in the beginning. It has exercises, and further readings(I advice checking out as well)

spacetimephysics - At eftaylor.com

The 1st and 2nd edition is also good; (my view that is)