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.)
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.
Problem Book in Relativity and Gravitation free 15
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.
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.
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.
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.
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.
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.
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).
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.
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.
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.
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.
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.
Two of the most tantalizing mysteries of modern astrophysics are known as the dark matter and dark energy problems. These problems come from the discrepancies between, on one side, the observations of galactic and extragalactic systems (as well as the observable Universe itself in the case of dark energy) by astronomical means, and on the other side, the predictions of general relativity from the observed amount of matter-energy in these systems. In short, what astronomical observations are telling us is that the dynamics of galactic and extragalactic systems, as well as the expansion of the Universe itself, do not correspond to the observed mass-energy as they should if our understanding of gravity is complete. Thus, this indicates either (i) the presence of unseen (and yet unknown) mass-energy, or (ii) a failure of our theory of gravity, or (iii) both.
There exists overwhelming evidence for mass discrepancies in the Universe from multiple independent observations. This evidence involves the dynamics of extragalactic systems: the motions of stars and gas in galaxies and clusters of galaxies. Further evidence is provided by gravitational lensing, the temperature of hot, X-ray emitting gas in clusters of galaxies, the large scale structure of the Universe, and the gravitating mass density of the Universe itself (Figure 1). For an exhaustive historical review of the problem, we refer the reader to [394].
Summary of the empirical roots of the missing mass problem (below line) and the generic possibilities for its solution (above line). Illustrated lines of evidence include the approximate flatness of the rotation curves of spiral galaxies, gravitational lensing in a cluster of galaxies, and the growth of large-scale structure from an initially very-nearly-homogeneous early Universe. Other historically-important lines of evidence include the Oort discrepancy, the need to stabilize galactic disks, motions of galaxies within clusters of galaxies and the hydrodynamics of hot, X-ray emitting gas therein, and the apparent excess of gravitating mass density over the mass density of baryons permitted by Big-Bang nucleosynthesis. From these many distinct problems grow several possible solutions. Generically, the observed discrepancies either imply the existence of dark matter, or the necessity to modify dynamical laws. Dark matter could, in principle, be any combination of non-luminous baryons and/or some non-baryonic form of mass-like neutrinos (hot dark matter) or some new particle, whose mass makes it dynamically cold or perhaps warm. Alternatively, the observed discrepancies might point to the need to modify the equation of gravity that is employed to infer the existence of dark matter, or perhaps some other fundamental dynamical assumption like the equivalence of inertial mass and gravitational charge. Many specific ideas of each of these types have been considered over the years. Note that none of these ideas are mutually exclusive, and that some form or the other of dark matter could happily cohabit with a modification of the gravitational law, or could even be itself the cause of an effective modification of the gravitational law. Question marks on some tree branches represent the fruit of ideas yet to be had. Perhaps these might also address the dark energy problem, with the most satisfactory result being a theory that would simultaneously explain the acceleration scale in the dark matter problem as well as the accelerating expansion of the Universe, and explain the coincidence of scales between these two problems, a coincidence exhibited in Section 4.1. 2ff7e9595c
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