These lectures represent an introductory graduate course in general relativity, both its foundations and applications. They are a lightly edited version of notes I handed out while teaching Physics 8.962, the graduate course in GR at MIT, during the Spring of 1996. Although they are appropriately called "lecture notes", the level of detail is fairly high, either including all necessary steps or leaving gaps that can readily be filled in by the reader. Nevertheless, there are various ways in which these notes differ from a textbook; most importantly, they are not organized into short sections that can be approached in various orders, but are meant to be gone through from start to finish. A special effort has been made to maintain a conversational tone, in an attempt to go slightly beyond the bare results themselves and into the context in which they belong.
The primary question facing any introductory treatment of general relativity is the level of mathematical rigor at which to operate. There is no uniquely proper solution, as different students will respond with different levels of understanding and enthusiasm to different approaches. Recognizing this, I have tried to provide something for everyone. The lectures do not shy away from detailed formalism (as for example in the introduction to manifolds), but also attempt to include concrete examples and informal discussion of the concepts under consideration.
As these are advertised as lecture notes rather than an original text, at times I have shamelessly stolen from various existing books on the subject (especially those by Schutz, Wald, Weinberg, and Misner, Thorne and Wheeler). My philosophy was never to try to seek originality for its own sake; however, originality sometimes crept in just because I thought I could be more clear than existing treatments. None of the substance of the material in these notes is new; the only reason for reading them is if an individual reader finds the explanations here easier to understand than those elsewhere.
Time constraints during the actual semester prevented me from covering some topics in the depth which they deserved, an obvious example being the treatment of cosmology. If the time and motivation come to pass, I may expand and revise the existing notes; updated versions will be available at http://pancake.uchicago.edu/~carroll/notes/. Of course I will appreciate having my attention drawn to any typographical or scientific errors, as well as suggestions for improvement of all sorts.
Numerous people have contributed greatly both to my own understanding of general relativity and to these notes in particular - too many to acknowledge with any hope of completeness. Special thanks are due to Ted Pyne, who learned the subject along with me, taught me a great deal, and collaborated on a predecessor to this course which we taught as a seminar in the astronomy department at Harvard. Nick Warner taught the graduate course at MIT which I took before ever teaching it, and his notes were (as comparison will reveal) an important influence on these. George Field offered a great deal of advice and encouragement as I learned the subject and struggled to teach it. Tamás Hauer struggled along with me as the teaching assistant for 8.962, and was an invaluable help. All of the students in 8.962 deserve thanks for tolerating my idiosyncrasies and prodding me to ever higher levels of precision.
During the course of writing these notes I was supported by U.S. Dept. of Energy contract no. DE-AC02-76ER03069 and National Science Foundation grants PHY/92-06867 and PHY/94-07195.