Syllabus

Course Meeting Times

Lectures: 2 sessions / week, 1.5 hours / session

Recitations: 1 session / week, 1 hour / session

Course Description

This course covers the basic principles of Einstein's general theory of relativity, differential geometry, experimental tests of general relativity, black holes, and cosmology.

Prerequisites

The course catalog lists Differential Equations (18.03), Linear Algebra (18.06), and Electromagnetism II (8.07) as prerequisites. Students should also be familiar with Lagrangians and action principles, Green's functions, and numerical analysis (some homework assignments require the numerical solution of systems of differential equations).

Textbooks

Required Text

Carroll, Sean. An Introduction to General Relativity: Spacetime and Geometry. San Francisco, CA: Addison Wesley, 2003. ISBN: 9780805387322.

Other Relevant Texts

General relativity is a subject that is either blessed or cursed (depending on your point of view) with an abundance of textbooks. Some of the ones I recommend for further reading are:

Misner, Charles W., Kip S. Thorne, and John Archibald Wheeler. Gravitation. San Francisco, CA: W.H. Freeman, 1973. ISBN: 9780716703440.
Universally known as MTW, a fantastic text if you already know GR thoroughly; rather intimidating if you are studying it for the first time. Still the best reference, in my opinion, for certain important topics; a few readings will be assigned from this volume.

Schutz, Bernard. A First Course in General Relativity. New York, NY: Cambridge University Press, 1985. ISBN: 9780521277037.
Gives very clear and careful introductory discussion of the mathematics that underlies general relativity.

Hartle, James. Gravity: An introduction to Einstein's general relativity. San Francisco, CA: Addison-Wesley, 2002. ISBN: 9780805386622.
A wonderful introduction to the subject, with the aim to get to important physical concepts as quickly as possible. As a consequence, Hartle jumps around a bit, deferring the introduction of some important quantities (such as curvature) to rather late in the text. This text is more elementary than I like for a graduate course, but is perfect for an undergraduate GR course.

Weinberg, Steven. Gravitation and Cosmology. New York, NY: Wiley, 1972. ISBN: 9780471925675.
There is perhaps no textbook in this subject that is held with such divergent views as this one. Many people love it because of the clarity of Weinberg's writing and presentation; quite a few hate it because of Weinberg's steadfast refusal to embrace wholeheartedly the notion of geometry as the central issue in GR. Weinberg does introduce and discuss the relevant geometric notions as appropriate, he just does not give them the starring role many people feel they deserve. Much like MTW, I find certain pieces of Weinberg's text to be fantastic; others less so. (In both cases, this is mostly due to the fact that these books were published over 30 years ago; the field and our ideas of how to teach it have advanced quite a bit since then.)

Wald, Robert. General relativity. Chicago, IL: University of Chicago Press, 1984. ISBN: 9780226870335.
The GR überbuch; typically the final arbiter of right and wrong in this subject. Quite mathematically sophisticated, and rather terse.

Poisson, Eric. A Relativist's Toolkit. New York, NY: Cambridge University Press, 2004. ISBN: 9780521830911.
The focus of this book is the machinery needed for advanced analysis of black holes. I am likely to use bits and pieces of Eric's analysis in 8.962.

Problem Sets

There will be a total of 11 problem sets. A problem set will be due almost every week; the exceptions are week 1, week 4, and week 11. Discussion on the problem sets is encouraged; the work that you hand in must, however, be your own. Each problem set is worth 6% of your total grade.

Final Exam

There will be an open book final exam, worth 34% of your total grade, scheduled by the Registrar and held during the Final Exam Period.

Grading Policy