The typical level of difficulty (especially mathematical) of the
is indicated by a number of asterisks, one meaning mostly introductory
and three being advanced. The asterisks are
normalized to these lecture notes, which would be given [**]. The
first four books were frequently consulted in the preparation of these
notes, the next seven are other relativity texts which I have found
to be useful, and the last four are mathematical background references.
- B.F. Schutz, A First Course in General Relativity (Cambridge,
1985) [*]. This is a very nice introductory text. Especially useful
if, for example, you aren't quite clear on what the energy-momentum
tensor really means.
- S. Weinberg, Gravitation and Cosmology (Wiley, 1972) [**].
A really good book at what it does, especially strong on astrophysics,
cosmology, and experimental tests. However, it takes
an unusual non-geometric approach to the material, and
doesn't discuss black holes.
- C. Misner, K. Thorne and J. Wheeler, Gravitation
(Freeman, 1973) [**]. A heavy book, in various senses. Most things
you want to know are in here, although you might have to work hard
to get to them (perhaps learning something unexpected in the process).
- R. Wald, General Relativity (Chicago, 1984) [***]. Thorough
discussions of a number of advanced topics, including black holes,
global structure, and spinors. The approach is more mathematically
demanding than the previous books, and the basics are covered pretty quickly.
- E. Taylor and J. Wheeler, Spacetime Physics (Freeman, 1992)
[*]. A good introduction to special relativity.
- R. D'Inverno, Introducing Einstein's Relativity (Oxford, 1992)
[**]. A book I haven't looked at very carefully, but it seems as if all the
right topics are covered without noticeable ideological distortion.
- A.P. Lightman, W.H. Press, R.H. Price, and S.A. Teukolsky,
Problem Book in Relativity and Gravitation (Princeton, 1975) [**].
A sizeable collection of problems in all areas of GR, with fully
worked solutions, making it all the more difficult for instructors
to invent problems the students can't easily find the answers to.
- N. Straumann, General Relativity and Relativistic Astrophysics
(Springer-Verlag, 1984) [***]. A fairly high-level book, which starts out
with a good deal of abstract geometry and goes on to detailed discussions
of stellar structure and other astrophysical topics.
- F. de Felice and C. Clarke, Relativity on Curved Manifolds
(Cambridge, 1990) [***]. A mathematical approach, but with an excellent
emphasis on physically measurable quantities.
- S. Hawking and G. Ellis, The Large-Scale Structure of
Space-Time (Cambridge, 1973) [***]. An advanced book which emphasizes
global techniques and singularity theorems.
- R. Sachs and H. Wu, General Relativity for Mathematicians
(Springer-Verlag, 1977) [***]. Just what the title says, although the
typically dry mathematics prose style is here enlivened by frequent
opinionated asides about both physics and mathematics (and the state
of the world).
- B. Schutz, Geometrical Methods of Mathematical Physics
(Cambridge, 1980) [**]. Another good book by Schutz, this one covering some
mathematical points that are left out of the GR book (but at a very
accessible level). Included are
discussions of Lie derivatives, differential forms, and applications to
physics other than GR.
- V. Guillemin and A. Pollack, Differential Topology
(Prentice-Hall, 1974) [**]. An entertaining survey of manifolds, topology,
differential forms, and integration theory.
- C. Nash and S. Sen, Topology and Geometry for Physicists
(Academic Press, 1983) [***]. Includes homotopy, homology, fiber bundles
and Morse theory, with applications to physics; somewhat concise.
- F.W. Warner, Foundations of Differentiable Manifolds and
Lie Groups (Springer-Verlag, 1983) [***]. The standard text in the field,
includes basic topics such as manifolds and tensor fields as well as
more advanced subjects.