Original by Chris Hillman (with contributions by Nathan Urban) September 1998.
You bet! There are dozens of superb, up-to-date books on various aspects of relativity theory. Most of these are currently in print and widely available through university libraries and organizations such as Amazon.com and Barnes & Noble. In addition, several classic books have recently come back into print. It is not an exaggeration to say that there has probably never been a better time to shop around for books on relativity!
In what follows I offer a sort of "consumer's guide" which I hope will help readers choose the book or books best suited to their needs. In addition to providing capsule reviews of a number of books I like, or which have been recommended by others whose judgement I trust, I have taken the liberty of warning the reader away from certain books, particularly (most of) the attractively priced but hopelessly outdated Dover reprints.
I have divided the discussion into seven broad categories:
There is a huge literature on "relativity for laypeople", most of which I cannot recommend. I can, however, name several books that I hope will not mislead the intelligent reader too badly.
Kip S. Thorne,
Black holes and time warps: Einstein's outrageous legacy.
W. W. Norton, 1995.
In print, ISBN 0-393-31276-3, list price $15.95 (paperback).
A delightful romp through the history of the notion of a black hole (a story in which Thorne has been an active participant). I doubt you'll wind up understanding very much relativity theory from reading this book, but you'll certainly have gained a vivid impression of some of the personalities involved in uncovering the mysteries of black hole physics. Note that Thorne is one of the triumvirate of authors of my favorite GTR textbook (see MTW below).
Robert Geroch,
General relativity from A to B.
University of Chicago Press, 1981.
In print, ISBN 0-226-28864-1, list price $12.95 (paperback).
As the title suggests, you can't expect to master a significant fraction of the basic notions of GR in this book, but what Geroch does cover here is very well explained. A beautifully illustrated and very gentle introduction to the geometry of Minkowski spacetime of SR and then to the curved spacetimes of GR, including a clear intuitive discussion of some features of Schwarzschild geometry (nonrotating uncharged black holes), by a leading physicist.
Robert M. Wald,
Space, time, and gravity: the theory of the big bang and black holes.
University of Chicago Press, 1992.
In print, ISBN 0-226-87029-4, list price $13.95 (paperback).
An excellent brief overview of relativity theory through the extraction of energy from black holes (the Penrose process), by a leading relativist.
Steven Weinberg,
The First Three Minutes: A Modern View of the Origin of the Universe. . .
Basic Books, 1988.
Out of print.
A delightful and very clearly written nontechnical survey of cosmology circa 1970, covering the Big Bang, Hubble expansion, cosmic microwave background radiation, observable universe and event horizons, and the "standard model" of cosmological nucleosynthesis, by one of the premier physicists of our time.
Clifford M. Will,
Was Einstein Right?: Putting General Relativity to the Test, 2nd ed.
Basic Books, 1993.
Out of print.
A nontechnical overview of how well the predictions of GR agree with experiment.
What about the well known book by Hawking, A Brief History of Time, you ask? To judge from the confusion it engenders in its readers (as reflected by numerous bewildered posts to this newsgroup mentioning some wild misunderstanding which is credited to this book), I cannot recommend this book.
I particularly recommend the first of the following books.
Edwin F. Taylor and John Archibald Wheeler,
Spacetime Physics: Introduction to Special Relativity, 2nd ed.
W. H. Freeman & Company, 1992.
In print, ISBN 0-7167-2326-3, list price $26.00 (hardcover)
This classic undergraduate textbook is simply the best introduction I know. It might look a bit hokey, but it's full of fabulous insights.
Wolfgang Rindler,
Introduction to Special Relativity, 2nd ed.
Oxford University Press, 1991.
In print, ISBN 0-19-853952-5; list price $32.95 (paperback)
Another reputable textbook, which I am not familiar with but which other posters have recommended in the past.
Anadijiban Das,
The Special Theory of Relativity: A Mathematical Approach.
Springer-Verlag, 1996.
In print, ISBN 0-387-94042-1; list price $39.95 (hardcover)
I am not familiar with this book, but it seems to be a concise but reasonably comprehensive and modern introduction, covering among other things the connection between Moebius transformations and the Lorentz group.
George F. Ellis and Ruth M. Williams,
Flat and Curved Space-Times
Oxford University Press, 1988
In print, ISBN 0-19-851169-8; list price $45.00 (paperback)
This book is notable for making a serious attempt to provide an introduction to both SR and GR, using only basic algebra and calculus (no tensors). It does treat some aspects of some exact solutions in GR but does not adequately cover the field equations and thus cannot be considered a suitable GR text. However, it may be helpful to the timorous reader attempting to make the transition from SR to GR.
Gregory L. Naber,
The Geometry of Minkowski Spacetime: An Introduction to the Mathematics of the Special Theory of Relativity.
Springer-Verlag, 1992.
In print, ISBN 0-387-97848-8; list price $65.95 (hardcover)
This book is devoted to a rigorous mathematical treatment of the flat Minkowski spacetime of special relativity. It pays particular attention to the Lorentz group and the causal structure of the theory, but also treats the electromagnetic field tensor, spinors, and the topology of Minkowski spacetime. This book won't teach you much physics, but is useful if you want to see special relativity put on a firm mathematical basis, or examine some of the more intricate technical implications of Lorentz transformations or SR causality.
I would not recommend the Dover reprint by Aharoni (outdated, poorly written, clumsy notation). I am not familiar with the Dover reprint by Shadowitz.
Now we are starting to get to the really good stuff! I label each of the following six textbooks with short codes and follow a brief review of each with a table comparing the topics they cover.
(DINV)Ray A. d'Inverno,
Introducing Einstein's Relativity
Oxford University Press, 1992
In print, ISBN 0-19-859686-3; list price $42.95 (paperback).
A beautifully illustrated, clearly and concisely written introduction to GR (the first few chapters, on SR, are too sketchy to be valuable except as a review). On balance, I think this is probably the best introduction for the average undergraduate student at present. It features a particularly well balanced selection of topics.
(SCH)Bernard F. Schutz,
A First Course in General Relativity
Cambridge University Press, 1985.
In print, ISBN 0-521-27703-5; list price $34.95 (paperback).
This book covers fewer topics than d'Inverno but in greater depth, and at a comparable level. In places I find it a bit more turgid than some other texts, but Schutz's discussion of the geometric nature of tensors in general and the matter tensor in particular is outstanding.
(STEP)Hans Stephani,
General Relativity: An Introduction to the Theory of the Gravitational Field, 2nd ed.
Cambridge University Press, 1990.
In print, ISBN 0-521-37941-5, $39.95 (paperback).
Probably a bit more demanding than d'Inverno, this is probably the best organized GR textbook yet to appear. Clearly written (and well translated from the original German), featuring a well balanced selection of topics, and full of useful insight.
(HT)L. Hughston and K. P. Tod,
Introduction to General Relativity
Cambridge University Press, 1991
In print, ISBN 0-521-33943-X; list price $23.95 (paperback).
One of the most concise introductions available. Covers much less than Stephani or d'Inverno, but clear and well written. Advanced undergraduate to beginning gradate level.
(WALD)Robert M. Wald,
General Relativity,
University of Chicago Press, 1984.
In print, ISBN 0-226-87033-2; list price $34.00 (paperback).
The textbook of choice for the discerning graduate student. Well written, with a good selection of topics, including careful discussions of tensor formalism, the basic singularity, stability, and uniqueness theorems, as well as black hole thermodynamics.
(MTW)Charles W. Misner, Kip S. Thorne, and John A. Wheeler,
Gravitation,
W. H. Freeman & Company, 1973.
In print, ISBN 0-7167-0344-0; list price $63.95 (paperback).
This huge (44 chapter), sprawling book is IMHO one of the great scientific books of all time, but may not the best ``first book'' on GR for most students, in part because by offering so much it is liable to overwhelm a newcomer. However, I think every serious student must own this at least as a supplementary text and dip into it on a regular basis. MTW was the first "modern" GR textbook, and has inspired two generations of students. While in many respects it is now rather out of date, and in a few places is pretty darn confusing, this beautifully illustrated book features fascinating insights found nowhere else on almost every one of its 1200-odd pages.
All of these books have exercises; DINV is particular well suited for self study since it also has solutions in the back. DINV and STEP give particularly good brief surveys of GR.
Overall, for timid readers, I'd recommend DINV, for bolder ones, STEP, for penurious students I'd recommend HT, for mathematically minded students I'd recommend WALD. And I'd recommend MTW to anyone, anywhere, any time. For really serious students, both WALD and MTW are probably essential references.
For the convenience of the rank beginner who wants to purchase one or more of these textbooks, here is a very rough guide to the coverage: all of these books introduce tensors, including the matter and Riemann and Ricci tensors. All discuss geodesics, connections and covariant derivatives. All discuss the Equivalence Principle, weak field theory, and at least one interpretation of the field equations. All discuss the classic predictions such as light bending, perihelion advance, gravitational redshift. Among the exact solutions, all discuss in some detail the "usual suspects" (Schwarzschild vacuum and Friedmann dust). All discuss the linearized theory of gravitational waves and Cartan's method of curvature forms.
Five of the six textbooks also discuss at length various of the following important topics: spinors, algebraic symmetries of tensors, the variational principle formulation of GR, the initial value formulation of GR, the Petrov classification of curvature types, EXACT gravitational wave solutions, the singularity theorems, Penrose diagrams (conformal compactification), Hawking radiation, and thermodynamics of black holes.
Sprs Sym VPF IVF Petrov GWves Sing PD Hawk Therm DINV X X X X x X STEP X X X X X x X HT X WALD X X X X X X X X MTW X X X X X X
Among exact solutions beyond "the usual suspects", DINV features detailed discussions of the Kerr-Newman vacuum, Reissner-Nordstrom electrovac, Tolman fluid, de Sitter and anti-de Sitter cosmological solutions. The Kasner dust is treated very nicely in HT, and STEP mentions the Bertotti-Robinson electrovac. HT also features a particularly clear and concise treatment of the Bianchi classification of homogeneous spacelike hyperslices.
While I think the six books listed above are among the best currently available textbooks, there are several others worthy of special mention.
Alan P. Lightman, William H. Press, Saul A. Teukolsky,
Problem Book in Relativity and Gravitation
Princeton University Press, 1975.
In print, ISBN 0-691-08162-X; list price $40.00 (paperback)
Since the only way to learn a mathematical theory is by doing problems, the more the merrier, this book is an invaluable resource for serious students.
J. Martin,
General Relativity: A First Course For Physicists
Prentice Hall, 1995.
In print, ISBN 0-13-291196-5; list price $37.95 (paperback).
Presents the bare essentials (geodesics, curvature, the field equation, "the usual suspects") in a concise and accessible manner. However, it uses coordinate notation exclusively, and thus cannot be considered a "modern" introduction (despite the date of publication), but it can be good place to learn the (essential!) coordinate methods of computation.
Paul A. Dirac,
General Theory of Relativity
Princeton University Press, 1996.
In print, ISBN 0-691-01146-X, list price $10.95 (paperback).
Yes, that Dirac. In his inimitable, incredibly concise style, Dirac offers a sixty page sketch of GR, with all the math but not a single picture. First published in 1975, this book doesn't cover any of the modern developments in the subject. If you are very impatient and have a very strong background in advanced calculus and some differential geometry, this just might be the right book for you. Otherwise it will sail right over your head. No exercises.
Hans C. Ohanian, Reno Rufkin and Remo Ruffini,
Gravitation and Spacetime, 2nd ed.
W. W. Norton, 1994.
In print, ISBN 0-393-96501-5; list price $43.50 (hardcover).
Most GR books follow more or less in Einstein's footsteps in motivating the field equation. These authors take a different approach which has become increasingly important in recent years; they motivate the linearized field equation by a careful formal analogy with Maxwell's theory of electromagnetism, and then argue their way to the full field equation. Strong on the important formal analogies with EM, but weak on geometry. It also has one of the best treatments to be found among introductory GR texts of the experimental and observational consequences of the theory, along with a nice discussion of newtonian gravity.
Gregory L. Naber,
Spacetime and Singularities: An Introduction.
Cambridge University Press, 1989.
In print, ISBN 0-521-33612-0; list price $24.95 (paperback).
In the same excellent London Mathematical Society Student Series as HT. I don't know this book but I've seen it somewhere; as I recall it looked somewhat forbidding.
C. Clarke,
Elementary General Relativity
Halsted Press, 1980.
Out of print.
A concise and readable introduction, emphasizing modern coordinate free notation. Has some good exercises.
Theodore T. Frankel,
Gravitational Curvature: An Introduction to Einstein's Theory.
W. H. Freeman & Company, 1979.
Out of print.
Features a particularly comprehensive introduction to the geometric meaning of the field equation, and a detailed introduction to relativistic optics. No exercises.
L. D. Landau,
The Classical Theory of Fields.
Course of Theoretical Physics, Vol. 2. Classical Theory
Butterworth-Heinemann, 1980.
ISBN 0-7506-2768-9; list price $47.95 (hardcover).
The first half is a concise introduction to SR and EM; the second half, an even more concise introduction to GR. Features a discussion of LeMaitre coordinates for the Schwarzschild solution and some other things not found in many other books. Some good exercises.
Dover has also reprinted books on relativity by the youthful Wolfgang Pauli, the mature Max Born, Peter Bergman, and Richard Tolman, which I feel are of marginal utility today, since they are very out of date and the topics they do discuss are IMO better explained in more modern language elsewhere. I would strongly recommend that students spend their money on more expensive but up-to-date textbooks.
The books by Schroedinger and Feynman are also entirely unsuitable for an introduction to GR.
In this section, I discuss some books that
I'll begin with several books in the Schaum's outline series, which, if read with discipline, can actually be a very effective way, I think, to learn some problem-solving skills. If you really are starting with linear algebra, however, you should expect to spend many months in hard labor working through these books before you are ready to being your study of GR. I am not familiar with all of the following books, but consider the one I own (the last) to be a good book.
Seymour Lipschutz,
Schaum's Outline of Linear Algebra, 2nd ed.
McGraw-Hill, 1991.
In print, ISBN 0-07-038007-4; list price $13.95 (paperback).
Frank Ayres and Elliot Mendelson,
Schaum's Outline of Calculus, 3rd ed.
McGraw-Hill, 1990.
In print, ISBN 0-07-002662-9; list price $14.95 (paperback).
Richard Bronson,
Schaum's Outline of Differential Equations, 2nd ed.
McGraw-Hill, 1994.
In print, ISBN 0-07-008019-4; list price $14.95 (paperback).
Paul C. DuChateau, and D. W. Zachmann,
Schaum's Outline of Partial Differential Equations
McGraw-Hill, 1986.
In print, ISBN 0-07-017897-6; list price $14.95 (paperback).
Murray R. Spiegel,
Advanced Mathematics for Engineers and Scientists.
McGraw-Hill, 1971.
In print, ISBN 0-07-060216-6; list price $14.95 (paperback).
Martin Lipschutz,
Differential Geometry.
McGraw-Hill, 1969.
In print, ISBN 0-07-037985-8; list price $12.95 (paperback).
A good introduction to classical differential geometry. Note well; for GR you need more advanced notions, including modern notions of manifolds, covariant, Lie, and exterior derivatives, connections, and curvature tensors.
David C. Kay,
Schaum's Outline of Tensor Calculus
McGraw-Hill, 1988.
In print, ISBN 0-07-033484-6; list price $13.95 (paperback).
An introduction to coordinate basis tensor computations, including the metric tensor, geodesics, the Riemann tensor, with applications to classical mechanics and SR (but not GR). This won't entirely get you up to speed for GR, but like the previous book it may be useful as a supplementary text.
John H. Hubbard,
Vector Calculus, Linear Algebra and Differential Forms: A Unified Approach.
Prentice Hall, 1998.
In print, ISBN 0-13-657446-7; list price $84.00 (hardcover).
This book can probably serve as a substitute for all of the Schaum's books mentioned above (save the last two), with the additional bonus of introducing exterior forms early on and properly emphasizing the fact that these objects are natural, easy to understand, and easy to compute with.
Theodore Frankel,
The Geometry of Physics: An Introduction.
Cambridge University Press, 1997.
In print, ISBN 0-521-38334-X; $95.00 (hardcover).
This book is simply gorgeous. It offers a thorough and beautifully illustrated introduction to everything from riemannian geometry, Cartan geometry, symplectic geometry, differential topology and Morse Theory to vector bundles and Pontryagin and Chern classes. Applications to hamiltonian mechanics, GR, Yang-Mills theories, the Standard Model of particle physics, etc., are also sketched.
Speaking of manifolds and differential geometry, I think that one of the best all around introductions is:
William M. Boothby,
An Introduction to Differentiable Manifolds and Riemannian Geometry, 2nd ed.
Academic Press, 1986.
In print, ISBN 0-12-116053-X; list price $58.00 (paperback).
One book which is particularly well suited for background reading in GR is the outrageously expensive
Barrett O'Neill,
Semi-Riemannian Geometry with Applications to Relativity.
Academic Press, 1983.
In print, ISBN 0-12-526740-1; list price $99.00 (hardover).
This book covers not only manifolds, tensors, metrics, connections, curvature, calculus of variations, homogeneous spaces, and covering spaces, but also Minkowski spacetime, the Friedmann and Schwarzschild solutions, and the singularity theorems.
Another classic, easy to read introduction is "the great American differential geometry book":
Michael Spivak,
A Comprehensive Introduction to Differential Geometry, 5 volumes.
Publish or Perish, 1979.
Vol. 1: ISBN 0-914098-84-5; $30.00
Vol. 2: ISBN 0-914098-85-3; $25.00
Vol. 3: ISBN 0-914098-86-1; $30.00
Vol. 4: ISBN 0-914098-87-X; $35.00
Vol. 5: ISBN 0-914098-88-8; $40.00 (all in hardcover only).
This book has a somewhat fussy notation, and tends toward the verbose, but it is engaging and full of insight. Boothby is shorter but covers more, although the last volume of Spivak is a gentle introduction to Chern classes.
A gentle introduction by popular author is:
Frank Morgan,
Riemannian Geometry: A Beginner's Guide, 2nd ed.
A K Peters, 1997.
In print, ISBN 1-56881-073-3; list price $34.00 (hardcover).
Another well known textbook (the author is a relativist) is:
Barrett O'Neill,
Elementary Differential Geometry, 2nd ed.
Academic Press, 1997.
In print, ISBN 0-12-526745-2; list price $49.95 (hardcover).
Another well known textbook (aimed more at hamiltonian mechanics) is:
R. Abraham, Jerrold E. Marsden, and T. Ratiu,
Manifolds, Tensor Analysis, and Applications.
Springer-Verlag, 1996.
In print, ISBN 0-387-96790-7; list price $69.95 (hardcover).
A cheaper alternative is:
Richard Bishop and Samuel Goldberg,
Tensor Analysis on Manifolds.
Dover, 1980.
In print, ISBN 0-486-64039-6; list price $8.95 (paperback).
At a higher level, try:
Y. Choquet-Bruhat, C. DeWitt-Morette, and M. Dillard-Bleick,
Analysis, Manifolds and Physics, Pt. I: Basics. Revised ed.
Elsevier Science, 1991.
In print, ISBN 0-444-86017-7; list price $63.50 (paperback).
Note that the first author has made important contributions to GR.
The most influential geometry book of all time is:
Shoshichi Kobayashi and Katsumi Nobizu,
Foundations of Differential Geometry. Two volumes.
John Wiley & Sons, 1996.
In print, ISBN 0-471-15733-3; list price $59.95 (paperback).
Not for the faint of heart.
A textbook by the greatest geometer of all time is:
Shiing-Shen Chern,
Differential Geometry.
World Scientific, 1998.
In print, ISBN 981-02-2647-0; list price $26.00 (paperback).
For the Russian perspective (one author is a legendary relativist), try:
B. A. Dubrovin, A. T. Fomenko, and S. P. Novikov,
Modern Geometry - Methods and Applications. 2 volumes, 2nd ed.
Springer-Verlag, 1993.
In print, ISBN 0-387-97663-9; list price $65.9a (hardcover).
I am not familiar with the following book, but I like an elementary GR text by the second author:
F. De Felice, C. J. Clarke,
Relativity on Curved Manifolds.
Cambridge University Press, 1992.
ISBN 0-521-42908-0; list price $42.95 (paperback).
Here are two pricey and extremely concise outlines of the basics of differential geometry and topology as they are used in modern physics:
M. Nakahara,
Geometry, Topology and Physics.
I O P Publishing, 1990.
In print, ISBN 0-85274-095-6; list price $61.00 (paperback).
Charles Nash and Siddartha Sen.
Topology and Geometry for Physicists.
Academic Press, 1988 (reprint).
In print, ISBN 0-12-514081-9; list price $58.00 (paperback).
These are so dense I wouldn't recommend them for anyone without a strong background in modern physics.
Dover has reprinted books by Levi-Civita, Schouten, and Synge on tensor calculus. These were all essential references in their day but they are now hopelessly out of date and I recommend that students spend their money on more expensive but more modern texts.
Here are some books that may help the student place relativity theory into the grand scheme of things, physically speaking:
I.D. Lawrie,
A Unified Grand Tour of Theoretical Physics.
I O P Publishing, 1990.
In print, ISBN 0-85274-015-8; list price $49.00 (paperback).
I like this book very much. Lawrie quite properly emphasizes the formal analogies between hamiltonian mechanics and quantum theory; the variational principle formulations of GR ties this relativity theory to both these subjects. Lawrie also emphasizes the fact that newtonian theory is not simply "wrong"; by a mere change of interpretation (and a factor of i here and a factor of h bar there) the equations of newtonian theory (as rewritten by Hamilton) go over to their quantum analogs. Needless to say these formal analogies are a great help to the working physicist.
Richard P. Feynman,
The Feynman Lectures on Physics
Addison Wesley Longman, 1970. 3 Volumes.
In print, available as boxed set or individual paperbacks.
One of the great scientific expositions of all time. Full of enthusiasm and overflowing with fabulous ideas. Feynman's geometric explanation of the physical meaning of Maxwell's equation is a joy; so is his discussion of action at a distance (his revolutionary work with Wheeler). The first two volumes are particularly recommended. Note well: in volume 2, the section on SR is one of the few weak points in the book; I advise that you skip it altogether. If you must read it, not, RPF is not saying that spacetime has a Euclidean metric!
L. D. Landau, E. M. Lifshitz and others,
Course of Theoretical Physics, 8 volumes.
Butterworth-Heinemann, various years.
Vol. 1 (Mechanics) and Vol. 2 (Classical Field Theory) are particularly relevant. Well translated and quite readable for the most part. Initiated by the great Russian physicist Lev Landau and continued after his untimely death by his disciple Lifshitz. The Russian approach to physics and math is significantly different from American ideas in many respects and it is worthwhile gaining some familiarity with Landau's vision. Unlike say Feynman's great books, this series offers many excellent exercises.
Walter Greiner and others.
A Curriculum in Theoretical Physics.
Springer-Verlag, various years.
Another heroic attempt to survey all of modern theoretical physics at the advanced undergraduate to second year graduate level, this time with a European perspective. Well translated from the German, very readable, with an excellent balance of theory, descriptions of "great experiments", and practical experience in computing things using the theory. Many exercises are solved in full.
Here are some books that relate relativity theory to important subjects in mathematics:
E. J. Flaherty,
Hermitian and Kahlerian Geometry in Relativity.
Springer-Verlag New York, 1976.
Out of print.
In Kahler geometry, instead of bundling tangent planes with a euclidean inner product, we bundle tangent planes with a hermitian inner product, which gives a much more "rigid" structure. However, symplectic geometry may be even more important in the future; see
M. Kauderer,
Symplectic Matrices, First Order Systems and Special Relativity.
World Scientific, 1994.
In print, ISBN 981-02-0829-4; list price $64.00 (hardcover).
Victor W. Guillemin and Shlomo Sternberg,
Symplectic Techniques in Physics.
Cambridge University Press, 1990.
In print, ISBN 0-521-38990-9; list price $37.95 (paper).
Helmut Hofer and Eduard Zehnder,
Symplectic Invariants and Hamiltonian Dynamics.
Birkhauser, 1994.
In print, ISBN 0-8176-5066-0; list price $59.50 (hardcover).
J. M. Souriau,
Structure of Dynamical Systems: A Symplectic View of Physics.
Birkhauser, 1997.
Out of print.
Dusa McDuff and Dietmar Salamon,
Introduction to Symplectic Topology.
Oxford University Press, 1995.
In print, ISBN 0-19-851177-9; list price $90.00 (hardcover).
A. T. Fomenko,
Symplectic Geometry, 2nd ed.
Gordon & Breach Publishing Group, 1995.
In print, ISBN 2-88124-901-9; list price $110.00 (hardcover).
Finally, for a glimpse of what quantum gravity may look like, try:
J. Baez and J. Muniain,
Gauge Fields, Knots and Gravity.
World Scientific, 1994.
In print, ISBN 981-02-2034-0; list price $43.00 (paperback).
This book also features an excellent and concise introduction to exterior forms and a good discussion of the rather vexed terms "contravariant" and "covariant" (they way they are used in older GR books is exactly opposite to their modern meaning in mathematics!) [From the editor (DK): But I think their use in older books makes much more sense!]
Here are some books of enduring historical interest:
Albert Einstein and others,
The Principle of Relativity
Dover, 1952 reprint.
In print, ISBN 0-486-60081-5; list price $7.95 (paperback).
A collection of historic papers by Lorentz, Einstein, and others, including Einstein's 1905 paper on STR, his 1907 paper on the equivalence of mass and energy, Minkowski's 1908 paper introducing the physical interpretation of his geometry, Einstein's 1916 paper on the foundations of GTR, and early attempts to unify EM and gravitation. In particular, the paper by Weyl laid the foundation for Yang-Mills theories, and the paper by Kaluza and Klein contains the idea of "compactified dimensions" which is a key element of modern string theories.
Hermann Weyl,
Space, Time, Matter
Dover, 1922.
In print, ISBN 0-486-60267-2; list price $9.95 (paperback).
Weyl was one of the great mathematicians of the early twentieth century, and one of the first to appreciate the importance of Einstein's ideas about gravitation and unified field theories. In this quirky but clearly written book, he describes the five year old theory of GR, assuming virtually no mathematical prerequisites, and attempts to go beyond it with ideas on non-riemannian connections which were several generations ahead of their time (in terms of physical application).
Richard C. Tolman,
Relativity, Thermodynamics and Cosmology
Dover, 1987 reprint.
In print, ISBN 0-486-65383-8; list price $13.95 (paperback).
An important resource in the thirties and forties but by now hopelessly out of date.
Arthur S. Eddington,
Space, Time and Gravitation: An Outline of the General Theory.
Cambridge University Press, 1987.
In print, ISBN 0-521-33709-7; list price $24.95 (paperback).
A classic semipopular book, by now hopelessly outdated, but written with the engaging, stylish verve that made Eddington one of the most popular science writers of his day.
Wolfgang Pauli,
Theory of Relativity.
Dover, 1981 reprint.
In print, ISBN 0-486-64152-X; list price $8.95 (paperback).
This was the first book on relativity theory, written in a burst of youthful enthusiasm by the twenty year old Pauli. Needless to say, it is of purely historical interest today.
Here is a book which is quirky but which will be valuable to some readers:
Richard P. Feynman,
Lectures on Gravitation.
Addison Wesley Longman, 1995.
In print, ISBN 0-201-62734-5; list price $38.43 (hardcover).
Feynman's attempt to motivate the field equation "in the spirit of QFT"; this approach is somewhat similar to that adopted in Ohanian et al, but this book is of interest mainly for watching Feynman at play.
Abraham Pais,
Subtle Is the Lord: The Science and Life of Albert Einstein
Oxford University Press, 1983.
In print, ISBN 0-19-520438-7, list price $17.95 (paperback)
This is the definitive scientific biography, written a noted physicist who personally knew Einstein, Bohr, and other key people in AE's career, and who has read every paper AE ever wrote. Features a fascinating, detailed—and fully technical—account of Einstein's heroic struggle toward his field equations.
Roberto Torretti,
Relativity and Geometry
Dover, 1996 (reprint).
In print, ISBN 0-486-69046-6; list price $14.95 (paperback).
This is another scientific biography focusing on the work rather than the man, offering some mathematical commentary on Einstein's struggle toward the field equation, and also discussing Einstein's "philosophy".
Don Howard and John J. Stachel,
Einstein: The Formative Years, 1879-1909
Birkhauser, 1998.
In print, ISBN 3-7643-4030-4, (price not available).
Another recent biography of Einstein.
John A. Wheeler and Kenneth Ford,
Geons, Black Holes, and Quantum Foam: A Life in Physics
W. W. Norton & Company, 1998.
In print, ISBN 0-393-04642-7, list price $27.95 (hardcover).
The autobiography of the physicist widely credited (along with Subrahmanyan Chandrasekhar) with transforming the notion of a black hole from dubious speculation into a common, and in some ways, quite well understood natural object.
The book by Kip Thorne (a former PhD student of Wheeler, who has had a distinguished career in his own right) cited above contains more information on the modern history of relativity.
N. T. Roseveare,
Mercury's Perihelion from Le Verrier to Einstein.
Oxford University Press, 1982.
In print, ISBN 0-19-858174-2; list price $49.95 (hardcover)
Features a detailed comparison of the GR prediction of precession with astronomical observation.
The following may also be of interest:
B. A. Rosenfeld,
The History of Non-Euclidean Geometry.
Springer-Verlag, 1988.
In print, ISBN 0-387-96458-4; list price $89.00 (hardcover).
Arthur J. Miller,
Albert Einstein's Special Theory of Relativity: Emergence (1905) and Early Interpretation, 1905-1911.
Springer-Verlag, 1997.
In print, ISBN 0-387-94870-8; list price $39.95 (hardcover).
D. Howard and J. J. Stachel,
Einstein and the History of General Relativity
Birkhauser, 1989.
In print, ISBN 0-8176-3392-8; list price $102.00 (hardcover).
J. Earman, M. Janssen, and J. D. Norton, editors,
The Attraction of Gravitation: New Studies in the History of General Relativity,
Birkhauser, 1993.
In print, ISBN 0-8176-3624-2; list price $150 (hardcover).
Who said history is cheap?
For a first book on the philosophical reaction to relativity, I'd recommend:
Lawrence Sklar,
Space, time, and spacetime.
University of California Press, 1974.
In print, ISBN 0-520-03174-1, list price $15.95 (paperback).
Engaging and delightful. This book won a prize for the exceptionally clear quality of its exposition. As a bonus, the later chapters contain an excellent nontechnical discussion of some of the features of the spacetime geometries treated in GR.
Hans Reichenbach,
Philosophy of Space and Time,
Dover, 1998
In print, ISBN 0-486-60443-8; list price $8.95 (paperback).
A reprint of a (well translated) classic book. Clearly written and highly influential.
Here are a few more recent books:
Lawrence Sklar,
Philosophy and Spacetime Physics
University of California Press, 1985.
In print, ISBN 0-520-06180-2; list price $13.00 (paperback).
Michael Friedman,
Foundations of Space-Time Theories: Relativistic Physics and Philosophy of Science.
Princeton University Press, 1983.
In print, ISBN 0-691-02039-6; list price $35.00 (paperback).
John Earman,
World Enough and Space-Time: Absolute vs. Relational Theories of Space and Time,
M.I.T. Press, 1989.
In print, ISBN 0-262-05040-4; list price $30.00 (hardcover).
I begin by listing three classic books that must be studied by every dedicated student of GR.
Stephen W. Hawking and G. F. Ellis,
The Large Scale Structure of Space-Time.
Cambridge University Press, 1975.
In print, ISBN 0-521-09906-4; list price $47.95 (paperback)
An extremely influential classic and a standard reference; this was the first book to provide a detailed description of the revolutionary topological methods introduced by Penrose and Hawking in the early seventies.
Roger Penrose and Wolfgang Rindler,
Spinors and Space Time: Two-Spinor Calculus and Relativistic Fields,
Cambridge University Press, 1984. Two Volumes.
Out of print.
Another standard reference, unfortunately out of print. This is the book that made Newman-Penrose tetrads and spinorial methods into a standard technique in the field.
S. Chandrasekhar,
The Mathematical Theory of Black Holes,
Oxford University Press, 1998.
In print, ISBN 0-19-850370-9; list price $29.95 (paperback)
By common consent, one of the great scientific books of our time. This is the book on black hole physics. Not for the faint of heart.
Robert M Wald, editor.
Black holes and Relativistic Stars.
University of Chicago Press, 1998.
In print, ISBN 0-226-87034-0; list price $50.00 (paperback)
This is the proceedings of the Chandrasekhar Memorial conference, and contains excellent survey articles by the leading experts in the field on all aspects of modern relativity theory. Particularly notable are the articles by Thorne (gravitational wave astronomy), Rees (astrophysical evidence for black holes), Penrose (censorship), Teukolsky (numerical relativity), Israel (internal structure of black holes), Wald (black hole thermodynamics), and Hawking (information paradox). Indispensable.
Here are four recent books focusing on various specialized topics of current interest:
Ignazio Ciufolini and John A. Wheeler,
Gravitation and Inertia.
Princeton University Press, 1995.
In print, ISBN 0-691-03323-4; list price $49.50 (hardcover).
Quirky, stylish, and inspiring. A little too concise for an introductory account, but the first half of this book features masterful summaries of the mathematical structure of GR and observational and experimental evidence. The remainder of the book focuses on Mach's principle, one of the oldest leitmotifs of GR.
Kip S Thorne, Richard H. Price, and Douglas A. Macdonald, editors. Black holes : the Membrane Paradigm.
Yale University Press, 1986.
In print, ISBN 0-300-03770-8; list price $21.00 (paperback)
One of the most important insights into black hole physics is that the event horizon can for many purposes be treated as a physical membrane made of a conducting material; this picture breaks down, of course, once you pass through the horizon, but it turns out to be very useful so long as you restrict yourself to physics occurring outside of the horizon. This should seem strange, because the event horizon is about as physically substantial as the International Date Line.
John Stewart,
Advanced General Relativity.
Cambridge University Press, 1993.
In print, ISBN 0-521-44946-4; list price $32.95 (paperback).
After a swift review of the basic notions of GR, this book focuses on the theory of gravitational wave detectors, a highly topical subject because of the expected advent of gravitational wave astronomy as workable detectors such as LIGO come on line in the next few years.
Robert M. Wald,
Quantum field theory in curved spacetime and black hole thermodynamics.
University of Chicago Press, 1994.
In print, ISBN 0-226-87027-8; list $16.95 (paperback).
John Baez considers this the premier book on semiclassical gravitation; Wald is perhaps the world's leading expert on black hole thermodynamics. Again, this is a topical subject indeed, as a glance at the Los Alamos preprint server at http://xxx.lanl.gov/ will reveal.
N. D. Birrell, and P. C. Davies,
Quantum Fields in Curved Space.
Cambridge University Press, 1984.
In print, ISBN 0-521-27858-9; list price $47.95 (paperback).
Many students prefer this to Wald's book because of the clarity of the writing and the excellent discussion of the particle concept.
S. A. Huggett and K. P. Tod,
An Introduction to Twistor Theory, 2nd ed.
Cambridge University Press, 1994.
In print, ISBN 0-521-45689-4; list price $22.95 (paperback).
In principle a beginning graduate level introduction to twistor theory, but I think most readers will find this book pretty tough going.
R. S. Ward and R. O. Wells,
Twistor Geometry and Field Theory.
Cambridge University Press, 1991.
In print, ISBN 0-521-42268-X; list print $42.95 (paper).
A more mathematical book, focusing on the Penrose transform and connections with representation theory.
Roger Penrose and Wolfgang Rindler,
Spinors and Space-Time. Two volumes.
Cambridge University Press, 1998 (reprint of 1986 edition).
Vol. I: out of print.
Vol II: in print, ISBN 0-521-34786-6; list price $52.95 (paperback).
The two volume book that founded twistor theory as a branch of mathematical physics. Not for the faint of heart.
Here are some more books on relativistic astrophysics:
I. D. Novikov, and Ya. B. Zel'Dovich,
Stars and Relativity.
Dover, 1996.
In print, ISBN 0-486-69424-0; list price $14.95 (paperback).
A reprint of a classic book (translated from the Russian) by the two most prominent Russian relativists.
Stuart L. Shapiro and Saul A. Teukolsky,
Black Holes, White Dwarfs, and Neutron Stars: The Physics of Compact Objects.
John Wiley & Sons, 1983.
In print, ISBN 0-471-87316-0; list price $97.95 (paperback).
Pricey, but a standard reference.
Barrett O'Neill,
The Geometry of Kerr Black Holes.
A K Peters, 1995.
In print, ISBN 1-56881-019-9; list price $88.00 (hardcover).
Also pricey, but this will surely be the standard book on Kerr geometry for a generation to come.
Steven Weinberg,
Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity.
John Wiley & Sons, 1972.
In print, ISBN 0-471-92567-5; $63.50 through discount outlets.
Another standard reference.
It is appropriate to close with three volumes from the collected works of the genius who first appreciated the reality of collapsed objects and black holes:
S. Chandrasekhar,
Selected Papers: The Mathematical Theory of Black Holes and of Colliding Plane Waves.
University of Chicago Press, 1991.
In print, ISBN 0-226-10101-0; list price $42.00 (paperback).
S. Chandrasekhar,
Selected Papers: Relativistic Astrophysics.
University of Chicago Press, 1990.
In print, ISBN 0-226-10099-5; list price $36.00 (paperback).
S. Chandrasekhar,
Selected Papers: The Non-Radial Oscillations of Stars in General Relativity and Other Writings.
University of Chicago Press, 1997.
In print, ISBN 0-226-10104-5; list price $45.00 (paperback).