They can often be quite useful for understanding particular
details of general relativity, its applications, or the associated
mathematics
I particularly recommend these first few books, all of which I have used as texts before:
Spacetime and Geometry, An Introduction to General Relativity, by Sean M. Carroll,
paperback, ISBN: 978-0805387322; Pearson (Addison-Wesley). This book is a greatly-expanded
version of Sean Carroll's earlier "Lecture Notes on General Relativity," which can still be acquired online, for free, from
a page on his current website. He notes that
about half of the book is newer than the lecture notes, that much of the material in the lecture notes was "polished
and improved" when the book was published, and that there are many more worked-out examples,
so that one should surely also purchase the book.
There is also quite an intriguing list of possible alternative ways to think about the universe and cosmology in a list of
(current) research interests of Carroll's, given at this link.
The text itself has especially good descriptions of Lie derivatives, and of Penrose diagrams, among other things, and his
section explaining the concept of manifolds is so good I could only wish I had written it.
Gravity: An Introduction to Einstein's General Relativity,
by James B. Hartle, Addison-Wesley, 2003.
This book labels itself as a discussion of the physically relevant solutions of the Einstein equation,
without first presenting derivations or too-sophisticated mathematics, as a course for junior- or senior-level
physics students. It does a good job of that, although does not present
enough understanding of the depth of
the material for my approach. It
also has a website, which has greater coverage of modern details, more
mathematical derivations, and some fine color photographs, as well as some
(Mathematica-based) computer-algebra programs to calculate connections and
curvatures.
A First Course in General Relativity, 2nd Edition, by Bernard Schutz, Cambridge Univ. Press, 2009.
It has very detailed introductions to some of the mathematics for differential geometry, and quite often good physical insights into what is "really" going on; however, occasionally he makes the reader work for that.
Gravity, from the ground up, by Bernard Schutz,
Cambridge Univ. Press, 2003.
This is a book with great quantities of words, and figures, trying to explain ALL
the interesting physical, and experimental, aspects of general relativity, with only
the physics that one would have picked up from an introductory first course in
physics, say at the level of Halliday, Resnick, and Walker. And it is written by
a well-acknowledged expert in the field!
The remaining books are listed in no particular order, but simply as I
wrote them down.
Gravitation, by Misner, Thorne and Wheeler;
W. H. Freeman &
Co., 1971.
Contained virtually everything known on the subject at the time
of its writing. Uses all the right sign conventions!
It is an excellent source for a review of special relativity,
in the first 9 chapters, and for a straightforward but detailed
approach to the mathematical foundations, in chapters 10-15.
Introduction to Special Relativity,
by Wolfgang Rindler, Oxford U., 1991.
A fine, physically-based introduction to many of the
details of special relativity.
Exact Space-Times in Einstein's General Relativity,
by Jerry B. Griffiths and Jiri Podolsky, 2009 Cambridge Univ. Press.
A detailed guide to the properties of many of the most important solutions of
Einstein's field equations, and guides to what "observers" in them might "see."
Gravitation and Spacetime, by Ohanian and Ruffini, Norton, 1994.
Supposed to be available to seniors;
it indeed does appear simpler, but I
haven't really studied it in great detail.
Introduction to General Relativity, by Adler, Bazin and Schiffer,
McGraw Hill, 1975.
An older, reliable book, with many good presentations, and
an excellent approach to the study of the Petrov types of solutions
to Einstein's field equations.
An Introduction to General Relativity and Cosmology, by Jerzy Plebanski
and Andrzej Krasinski, Cambridge Univ. Press, 2006.
Quite recent, and put together by an expert in the set of all cosmological
solutions of the Einstein field equations. Has detailed discussions of the
Lemaitre-Tolman cosmologies which are not homogeneous, and their relations
to the data known at the time of writing, which definitely includes the
moderately-recent supernovae data.
General Relativity, by Robert Wald, U. Chicago Press, 1984.
A good textbook, from a writer with a good physical intuition, but unwilling to use the
most modern forms of mathematics, that are used by many more writers today than when he
first wrote this text. He also uses something called the abstract index notation,
which in my experience is difficult to learn, although perhaps convenient after that learning
curve has been survived. Its cosmology is of course quite dated by now.
Relativity and Cosmology, by Robertson and Noonan, Saunders, 1968.
Again older but reasonable; has excellent presentations of the
electromagnetic field.
General Relativity and Gravitation, A Centennial Perspective, edited by Abhay Ashtekar,
Beverly K. Berger, James Isenberg, and Malcolm MacCallum, Cambridge Univ. Press, 2015.
A collection of the latest thoughts on many subjects, each written by an expert in that sub-field, and
quite up to date, both theoretical and experimental!
Gravitation and Cosmology, by Steven Weinberg, John
Wiley, 1972.
While this is an older book, and also uses only older tensor-style
notation, it has an excellent section on Lie derivatives and
symmetries,
and is certainly one of the most detailed beginning references for
a physicist's approach to cosmology.
Principles of Physical Cosmology, by P.J.E. Peebles,
Princeton U., 1993.
Very good astronomer's approach to cosmology, with lots of discussion
about real measurements from real data. As well, tries to integrate
it with theoretical general relativity. [Note that this is the 1993
edition; the earlier edition did not do any of this integration!]
Theory and experiment in gravitational physics, by Clifford Will,
Cambridge U., 1981. Excellent discussions of all experiments known
at that time, with mathematics only as needed.
Problem book in relativity and gravitation, by Lightman, Press,
Price and Teukolsky, Princeton U., 1975.
Worked out problems to go along with
the ordering of the text by Misner, Thorne and Wheeler.
Exact Solutions to Einstein's
Field Equations: Second Edition, by Stephani, Kramer, MacCallum,
Hoenselaers, and Herlt. (Cambridge Univ. Press, 2003)
While it is quite advanced, and detailed, this book is recent and contains
both a detailed summary of the majority of the known solutions of Einstein's
field equations and concise summaries of what one needs to know in order to
understand those solutions. Therefore, there
are quite a lot of interesting things to look at, especially in the early
parts.
The large scale structure of space-time, by Hawking and Ellis,
Cambridge U., 1973.
The standard basic reference for details of problems
concerning singularities in general relativity.
Has very good, brief descriptions of both deSitter
and anti-de Sitter universes, with comments concerning their use
as cosmologies.
Special Relativity in General Frames, From Particles to Astrophysics, by Eric
Gourgoulhon, Springer. 2013.
Very carefully describes the use of special relativistic kinematics, dynamics, electromagnetism, and
particle physics in arbitrary reference frames. These frames may be linearly accelerating, rotating,
or other more complicated things.
Advanced General Relativity, by John Stewart, Cambridge,
1990.
This book has 2 chapters on advanced aspects of some mathematis
that is useful in relativity, namely some modern approaches to
tensor theory (also known in that case as differential geometry),
and a very good approach to spinors. It then has 2 chapters on
global properties of solutions of the field equations, especially
relating to limits very, very far from sources, and on how you
begin a problem---with Cauchy data.
Group Theory and General Relativity, by Moshe Carmeli,
McGraw-Hill, 1977.
Has excellent discussions of the representations of the (complex)
Lorentz group, the relationships of this to spinors in general
relativity, and details of the Bondi-Metzner-Sachs group, which
is an important way to try to understand the physical content of
newly-discovered solutions of the field equations.
The Mathematical Theory of Black Holes, by Chandrasekhar, Oxford
U., 1992.
An advanced, and very well presented approach to this problem,
including details of perturbative calculations for applications to real
world astrophysics.
Physics of Black Holes, by Novikov and Frolov, Kluwer, 1989.
The best source for astrophysical applications, up to that time.
Black Holes and Time Warps, by Kip Thorne, Norton, 1994.
A history
of science, discussing the evolution of these ideas by a person who was
intimately involved in much of it; highly readable, but no mathematics.
Black Holes and Relativistic Stars, edited by Robert M.
Wald, U. Chicago Press, 1998.
Being the talks at a conference honoring the work of Chandhrasekhar.
A lot of it is quite general overviews of current research efforts, and
therefore quite interesting.
Essential Relativity, by Wolfgang Rindler, Springer-Verlag, 1979.
A very nice discussion of the attitude the title takes, to both special
and general relativity, with considerable physical insight.
Introduction to General Relativity, Black Holes & Cosmology, by
Yvonne Choquet-Bruhat, Oxford Univ. Press, 2015,
This is the very best place to have full mathematical rigor in these discussions.
The author is an acknowledged expert in the Cauchy problem.
Gravitation, Foundations and Frontiers}, by T. Padmanabhan,
hardback, ISBN: 978-0521882231 ; Cambridge Univ. Press
It has a nice, simple discussion of the Thomas precession in special relativity, and some approaches
to the evolution of perturbations in the universe, which are the best I have seen anywhere. In addition, it also provides
an understanding of what it means to say
that gravity is an "emergent" theory, and some (older) introductions to quantizing gravity. The emphasis is always based on
trying to agree with, and explain, the observations. It is unfortunate that it does not have the very latest material on the
Buchert equations concerning difficulties with averaging nonlinear processes (relevant to the possibility of "dark energy.")