Math 592D: General Relativity
Spring 2010
Einstein's general theory of relativity is the best available theory of
gravity at this time, and it is a centerpiece of modern physics and
astronomy. From a mathematical and aesthetic perspective, it is
the gold standard for what a physical theory should be. It may be
learned as a branch of physics or of mathematics.
This interdisciplinary course is designed for math and physics graduate
students, but it is also open to highly motivated, advanced
undergraduates. The course will begin with a rapid
introduction to special relativity, then develop some of the essential
mathematical machinery of differential geometry. The main topics
of the course will be the Einstein field equations and the spacetime
geometry of the vacuums surrounding Schwarzschild and Kerr black holes
and stars. Additional topics may include cosmology,
gravitational waves, interior Schwarzschild solutions (as models
of stars), electromagnatism in general relativity, and/or other more
advanced subjects depending on available time and class
interests.
Prerequisites:
For
Math Students: Math 462 and Math 350
For Physics Students: Phys 402,
Phys 410 (the prerequisites for Phys 640)
Also recommended for math students as
background or co-requisites are any courses from the following list:
Math 501, Math 450, Math 550, Math 571.
Textbook: The main textbook for
the course is General relativity: an
introduction for physicists, by Hobson, Estanthiou, and
Lasenby. Mathematical topics in the text will be supplemented by
lectures.
Additional References:
There are many excellent books on general relativity that can be used
as references or for supplemental reading. Among these are (with
elementary texts listed first):
The Geometry of Spacetime: An
Introduction to Special and General Relativity, by James
Callahan
A short course in general relativity,
by J. Foster and J. D. Nightingale
A first course in general relativity,
by Bernard Schutz
An introduction to general
relativity: spacetime and geometry, by Sean Carroll
Gravitation, by Misner,
Thorne, and Wheeler
General Relativity, by Robert
Wald
Semi-Riemannian geometry with
applications to relativity, by Barrett O'Niell
General relativity for mathematicians,
by R. K. Sachs and H. Wu