General Relativity UK ed. Edition

The first book I use for GR was Schutz, that is a wonderful book on its own but is only as it is named "A first course". Then I went through Carroll, to be honest GR has never been an easy one for me. Having said that I believe to had acquire a better mathematical and physical maturation for when I decided to pick Wald. I like the tensorial notation used, also it has the best derivation of Einstein's equations I have come across so far, I would say much, much better than Carroll's one, it is also self contained and I like the mathematical level used throughout. It consists of two parts, part one called FUNDAMENTALS has 6 chapters, part two titled ADVANCED TOPICS continues from chapter 7 till 14, I have studied chapters 1-13: Introduction, Manifolds and Tensor Fields, Curvature, Einstein's Equations, Homogeneous Isotropic Cosmology, The Schwarszchild Solution, Methods for Solving Einstein's Equations, Casual Structure, Singularities, The Initial Value Formulation, Asymptotic Flatness, Black Holes, Spinors. The only chapter I have not read yet because of lack of time is the last Chapter 14 "Quantum Effects in Strong Gravitational Fields". What I most like of this book is the crystal clear explanatory level that R. Wald shows through out the entire material making evident that he is a brilliant expositor and teacher, for example, is the first time that I really understood the singularity theorems of Penrose and Hawking (mathematically), also for the Initial Value Formulation chapter, he provides and explains what is needed in the theory of partial differential equations which motivated me even further to look at another book to go more in depth into partial differential equations and their relations with GR; and just for the last example the "Spinors" chapter is a tour de force which after going through it made me (I believe) understood everything about the representations of the Poincare group and things like why the Klein Gordon equation describes a unitary representation of the Poincare group acting on physical states of spin zero, Dirac's equation acts on particles of spin 1/2, Maxwell's acts on particles of spin 1 and (linearized) gravity on particles of spin 2. As if this were not enough it also brings 6 Appendices which complement the whole book! All in all the best book on GR I have come across so far, I also prefer it much more rather than Weinberg.

This book is a classic, and shall continue to be a classic for many years. It covers essencially every topic in advanced general relativity, and of course covers the basics. However, this is not a book for a first contact with general relativity. Having studied books such as Hartle's or Carroll's, and then studied a little of manifold theory (geometric construction of tensors, connections, etc) one may proceed to Wald's text. Even the introductory sections, which are not its focus, are great, and the discussions regarding both the physical point of view and their mathematical translation are very precious. I also like the way it derives the Schwarzschild solution, being the only book I know so far which indeed starts from the symmetries of the Schwarzschild spacetime - other books usually start with a set of preferred coordinates, a good ansatz, and use the Einstein equations to obtain the unknowns. Maybe one of the only things I don't like about this books is its notation, a little bit old-fashioned.Its mathematics is powerful, and just reading the appendixes is not enough. One must look for other sources as well, in particular in the chapter of differential forms and integration.My advice is: learn all the physics, with its beauty and power to solve problems, from Hartle; read some of Carroll's notes on the go, because they are a little more mathematical; learn the necessary mathematics from somewhere else; and then proceed to Wald's book. For problems and exercises, I recommend Lightman's "Problem Book in Relativity and Gravitation".

Hands down the best GR textbook I have ever read! The appendix on Lagrangian and Hamiltonian formulation has been incredibly clear for me and has helped me tremendously. I find Wald has done what I always want a physics text to do. He is mathematically rigorous enough to fully derive things properly while bot getting too bogged down in trying to prove ever little statement of differential geometry theorem. This allows the reader to fully understand the precise mathematics that one need if they want to look further into subject, and still understand the physical reasoning behind everything. While this was my first GR text, I would not recommend that they use this book as an introduction to the field. It is quite mathematical in its approach and can be a little overwhelming in the beginning. The only downside of the text is the beginning differential geometry section which moves very quickly and can be a little confusing at parts (at least for me). The initial value problem section is also very helpful in not just understanding GR but initial value problems (pde) in general physics.

I have owned this book (the paper version) for over twenty years. It is the best "modern" textbook on general Relativity. Differently from other books, the derivations are both clear AND rigorous. The book presents a complete discussion of the Schwarzschild solution and the derivation of results that can be used to test GR. Modern tests, like the slowing down of radar signals (first tested in experiments using the Mariner space probe), are discussed in detail. However, this text is not up to date. It needs to be complemented by a more modern book. "Modern General Relativity: Black Holes, Gravitational Waves, and Cosmology 1st Edition by Mike Guidry (Author)" is a possible choice.

If you're looking for a book to take you through the derivations and implications of GR, this is the book for you. That said make sure your understanding of manifold theory, geometry, and tensor mathematics are up to snuff. This is not a book for beginners.