Mathematics 236/Physics 292: General Relativity (Fall 2002)
Instructor
Arlie Petters
Description
Introduction to the basic concepts and techniques of
General Relativity. The course will cover the fundamentals of tensor
calculus, Lorentzian geometry, and Einstein's equations, as well as
applications to cosmology, black holes, and gravitational lensing. Each
student will write a paper selected from a list of topics tailored to the
student's mathematics and/or physics background --- e.g., physics topics
may include acceleration of the universe, the large-scale structure of
matter in the universe, detection of extra-solar planets, dark matter
reconstruction, gravitational waves, etc.; mathematics topics may involve
Lagrangian and Hamiltonian methods, positive energy theorems, cosmic
censorship, the Morse inequalities and multiple lensed images, Euler's
characteristic and the geometry of caustics, etc.
This is a core course for students who want to work in classical gravity,
cosmology, gravitational lensing, theoretical astrophysics, string theory,
or related subjects.
COURSE OUTLINE (tentative):
I. Manifolds and Tensors
- Tangent vectors and differential maps
- Curves, vector fields, and one-forms
- Tensor fields and the abstract index notation
II. Lorentzian Geometry
- Covariant derivatives and parallel transport
- Curvature and geodesics
- Computing curvature
III. The Einstein Field Equations
- General and special covariance
- Einstein's equations and the cosmological constant
- The weak-field limit
IV. Applications
- Big Bang cosmology
- Black holes
- Gravitational lensing
- Additional topics depending on time availability
Textbooks
-
Robert M. Wald,
General Relativity
(University of Chicago Press, Chicago, 1984).
-
A. O. Petters, H. Levine, and J. Wambsganss,
Singularity Theory and Gravitational Lensing
(Birkhauser, Boston, 2001).
Prerequisites
A basic facility with Multivariable Calculus (Math 103)
and Linear Algebra (Math 104).
Course Website
For more information see http://www.math.duke.edu/~petters/mth236-GR.html .
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Last modified: 16 March 2002