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8.962 :: General Relativity |
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About this class
8.962 is MIT's graduate course in general relativity. The course
catalog lists 18.03 (differential equations), 18.06 (linear
algebra), and 8.07 (electricity and magnetism) as prerequisites.
Students should also be familiar with Lagrangians and action
principles, Green's functions, and numerical analysis (some
homework assignments will require the numerical solution of systems
of differential equations).
Lectures
Recitation
Staff
Lecturer: Prof. Scott Hughes. Office: 37-626C; Telephone 8-8523; sahughes@mit.edu.
Recitations: Mr. Will Farr. Office: 37-624C; farr@mit.edu.
Office hours
No formal standing office hours, but happy to meet with students
by appointment. Please email Scott or Will if you want to get
together.
Required text
An Introduction to General Relativity: Spacetime and
Geometry, Sean Carroll.
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.
Speaking for myself (Hughes), I love none of these textbooks
(including the required text), but rather find that all have
strong points and weak points. Carroll's text does a nice job
hitting all the main points needed (especially for a 1 semester
class), and does so using language and notation that is
up-to-date. There are several other texts that you should be
aware of.
These texts are on reserve at the physics reading room (4-365):
Gravitation, Misner, Thorne, and Wheeler; universally
known as MTW. A nice reference once you already know GR
thoroughly; not so great if you are studying it for the
first time. Very good for certain important topics (e.g.,
spherically symmetric stars, black holes); a few recommended
readings are taken from this volume. Carrying this textbook
around for several weeks is an excellent way to strengthen
your lower back.
A first course in general relativity, Bernard
Schutz. Gives very clear and careful introductory discussion
of the mathematics that underlies general relativity. Many
of the first (foundational) lectures in this class have
their roots in Schutz's discussion.
Gravity: An introduction to Einstein's general
relativity, James Hartle. 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, defering 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.
The texts listed below are not on reserve, but are
nonetheless important and worthwhile. Depending on your level of
interest, you may find it useful to consult them.
Gravitation and Cosmology, Steven Weinberg. This
textbook was originally published at almost the same time as
MTW; as a consequence, several generations of GR students
were educated using either MTW or Weinberg. Takes a rather
different point of view, trying to avoid becoming enraptured
by the notion of geometry. Instead, Weinberg presents GR,
as much as possible, as a classical field theory like any
other. Time has not been terribly kind to this viewpoint,
so this text is now considered somewhat deprecated.
Nonetheless, it is beautifully written and very clear.
Worth knowing.
General relativity, Robert Wald. The GR
überbuch; typically the final arbiter of right and
wrong in this subject. Quite mathematically sophisticated,
and rather terse. A few pedagogical gems are hidden here
(e.g., the nicest proof of the Bianchi identity I've ever
seen).
A Relativist's Toolkit, Eric Poisson. The focus of
this book is the machinery needed for advanced analysis of
black holes. Also contains some gems, particularly in the
synopsis of GR. I use bits and pieces of Eric's analysis in
8.962.
Homework and grades
There will be 11 problem sets, due at the beginning of
class on Thursday in the classroom (3-343). No late
homeworks will be accepted without making prior arrangements
with either Hughes or Farr. We're both pretty easygoing, so
any reasonable request for an extension is likely to be granted
--- just do us the courtesy of letting us know in advance.
There will be a problem set due almost every week; the
exceptions are week 1 (Feb 7), week 4 (Feb 28, following a week
with only 1 lecture), and week 12 (May 1, following a week with
only 1 lecture).
Discussion on the psets is encouraged; the work that you hand in
must, however, be your own. You are of course welcome to
consult the course staff with questions.
Each pset except the final one is worth 9% of your total grade;
pset 11 is worth 10%. There will be no final exam.
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