4H General Relativity Page
Lecturer: Simon Ross
The topic of this course is the classical relativistic theory of
gravity, general relativity. This is a geometric theory: the key
idea is that gravity is a consequence of the curvature of
space-time.
The course will consist of a brief review/introduction of
special relativity, followed by a discussion of the differential
geometry which provides the mathematical underpinning to the
description of gravity as the curvature of spacetime. We will then
discuss the field equations of general relativity, and explore the
physical properties of interesting simple solutions, describing
black holes, cosmology, and gravitational waves.
If you have questions about the course, do send me e-mail, or come and see
me in my office, CM 218. (Suggestions for the web page are also
welcome.)
Syllabus for the first term:
- Introduction to general relativity - gravity as geometry
(1)
- Special relativity - spacetime diagrams, line element,
vectors and tensors, stress-energy tensor (4)
- Manifolds - spacetime is a manifold, coordinates,
tensors revisited, metric, integration on manifolds (6)
- Covariant derivative - necessity, connection, parallel
transport, geodesics (3)
- Curvature - Riemann tensor, flatness, commutation of
derivatives, tetrads, geodesic deviation (4)
Syllabus for the second term:
- General relativity - Equivalence principle, physics in
curved spacetime, Einstein's equations, Einstein-Hilbert action
(6)
- Black holes - Spherical symmetry, Schwarzschild
solution, geodesics, solar-system applications, event horizon and
Kruskal coordinates, black hole formation (8)
- Cosmology - Isotropy and homogeneity, FRW metric,
examples of cosmologies, Hubble law, particle horizons (6)
Books
The course will follow the lecture notes by Carroll most closely,
but I expect to draw on all these books at one time or another. I
mention only the books that I tend to use myself; there are many
other good ones. Jim Hartle has a more physics-oriented
introductory book in preparation; it would be worth getting when it
appears. The books are listed in something like order of increasing
difficulty.
- B.F. Schutz, A First Course in General Relativity,
Cambridge (1985): A good introductory book, with a pleasant
discursive style.
- R. D'Inverno, Introducing Einstein's Relativity, Oxford
(1992): Another introductory book, with somewhat more meat. A good
book for independant study. May be useful for those who want to
know a little more about topics I cover lightly.
- S. Carroll, Lecture Notes on
General Relativity, gr-qc/9712019: A
very clear and complete set of lecture notes, with a good balance
between mathematics and physics.
- R.M. Wald, General Relativity, Chicago (1984): A
personal favorite, despite the somewhat brief treatment of some of
the introductory topics. Good discussions of advanced topics of
current interest.
Problem sets
Problem sheet: 1up postscript 2up postscript
Also watch for typo corrections.
Useful web links
All the relativity-related links one could ever want are at the
Syracuse relativity bookmarks. Carroll's lecture
notes were already mentioned above. There's an excellent
guide to black holes (produced by an undergraduate at
Syracuse). For further reading once you've learned the basics, I
recommend the journal
Living reviews in relativity, which publishes web-based reviews
of current fields of interest in relativity, and matters of
gravity, an electronic newsletter with descriptions of current
events.
Etc...
Plot of scales in gravity from the first
lecture, from Gravitational Physics:
Exploring the Structure of Space and Time, (National Academies
Press, Washington, DC 1999)
Plots of the effective potential for
geodesics in the Schwarzschild spacetime and in a Newtonian
gravitational field.
Back to my home page
Back to the
lecture course schedule
Simon Ross (S.F.Ross@durham.ac.uk)
Last modified on Sept 28 1999