General Relativity
(Math 236 and Physics 292)
Spring 2010
Official Capacity
information
Instructor:
Paul Aspinwall
Credits: 1.0, Hours: 3.0
Time: MWF 3:05PM-3:55PM
Location: Physics 205
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 general relativity,
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 is desirable
too.
Exams
There will possibily be a mid-term exam. A take-home final will be
given which will be due in on Friday, May 7 at 10:00pm.
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. Riemannian Geometry
- Covariant derivatives and parallel transport
- Curvature and geodesics
- Computing curvature
III. The Einstein Field Equations
- General and special covariance
- Einstein's equation
- The weak-field limit
IV. Applications
- Cosmology
- Robertson-Walker universes
- The cosmological constant (“dark energy”)
- The Schwarzschild solution
- Gravitational red shift
- Black holes
- Perihelion precession and bending of light
- The Kruskal extension
- Further Analysis of Black Holes
- The Reissner-Nordström Solution
- The Kerr Solution
- The Ergosphere
- Black Hole Thermodynamics
Textbooks
The course will be based on the text:
- Robert M. Wald,
General Relativity, University of Chicago Press, Chicago, 1984.
See also
- Sean M. Carroll, Spacetime and Geometry, An Introduction to
General Relativity, Addison Wesley 2004. (See also
gr-qc/9712019
for what might be considered to be an earlier form of this book online.)
- Mark Trodden and Sean M. Carroll, TASI Lectures:
Introduction to Cosmology,
astro-ph/0401547.
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