General Relativity
(Math 236 and Physics 292)
Spring 2004
Official Capacity
information
Instructor:
Paul Aspinwall
Credits: 1.00, Hours: 03.0
Time: MWF 2:20-3:10
Location: Physics 228E
Requirements
Description
Introduction to the basic concepts and techniques
of General Relativity. The course will cover the fundamentals of
tensor calculus, Riemannian geometry, and Einstein's equations, as
well as applications to cosmology and black holes.
This is a core course for students who want to work in classical gravity,
cosmology, gravitational lensing, theoretical astrophysics, string theory,
or related subjects.
Homework
Prerequisites
A sound knowledge of multivariable calculus (at
least Math 103) and linear algebra (at least Math 104). A basic
knowledge of classical mechanics and electromagnetism would be very
useful too.
Exams
TBA
Synopsis
A rough tentative outline is as follows.
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
- Additional topics depending on time availability
Textbooks
The course will be based on the text: - Robert M. Wald,
General Relativity, (University of Chicago Press, Chicago, 1984).
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