Instructor
The instructor for this course is Eric Poisson. My office is
MacNaughton 211 on the Guelph campus, my phone number is (519)
824-4120 x53991, and my e-mail is
epoisson@uoguelph.ca.
Classes will meet on Wednesdays at the Perimeter Institute for
Theoretical Physics, starting on January 11, 2012. The first class
meeting is from 10:00 to 11:30 om the Alice Room. The second class
meeting is from 3:30 to 5:00 also in the Alice Room.
The recommend textbook for the course is
- Eric Poisson, A relativist's toolkit: The mathematics of
black-hole mechanics
(Cambridge University Press, Cambridge, 2004; QC 173.6.P65).
- S.M. Carroll, Spacetime and geometry: An introduction to
general relativity
(Addison Wesley, San Francisco, 2004; QC 173.6.C377).
- J.B. Hartle, Gravity: An introduction to Einstein's general
relativity
(Addison Wesley, San Francisco, 2003; QC 173.6.H38).
- R. d'Inverno, Introducing Einstein's relativity
(Clarendon Press, Oxford, 1992; QC 173.55.D56).
- C.W. Misner, K.S. Thorne, and J.A. Wheeler, Gravitation
(Freeman, New York, 1973; QC 178.M57).
- B.F. Schutz, A first course in general relativity
(Cambridge University Press, Cambridge, 1985; QC 173.6.S38).
- R.M. Wald, General relativity
(University of Chicago Press, Chicago, 1984; QC 173.6.W35).
- S. Weinberg, Gravitation and cosmology
(Wiley, New York, 1972; QC 6.W47).
There are no formal prerequisites for this course. However, this is an
advanced course on general relativity and it is assumed that
you are familiar with the basic elements of the theory. You may, for
example, have taken an introductory course before. Or you may have
studied an introductory book, for example the books by Schutz, Hartle,
or Carroll listed previously.
Grades will be based on homework assignments (60%) and
a term project (40%).
Homework problems will be given out every second or third week. The
term project will consist of a term paper on a topic of your choice
related to general relativity, together with a 20-minute presentation
on this topic. You must submit your topic to me before
February 8. I require a few paragraphs explaining what you
intend to do. It will my decision whether your topic is suitable for a
term paper. The presentations will be scheduled during the last weeks
of the semester.
I will select among the following topics, and perhaps insert
additional topics as well.
-
Fundamentals
1- Vectors, dual vectors, and tensors. 2- Covariant differentiation.
3- Geodesics. 4- Lie differentiation. 5- Killing vectors. 6- Local
flatness. 7- Metric determinant. 8- Levi-Civita tensor. 9-
Curvature. 10- Geodesic deviation. 11- Fermi normal coordinates.
-
Geodesic congruences
1- Energy conditions. 2- Kinematics of a deformable medium.
3- Congruence of timelike geodesics. 4- Congruence of null
geodesics.
-
Hypersurfaces
1- Description of hypersurfaces. 2- Integration on hypersurfaces.
3- Gauss-Stokes theorem. 4- Differentiation of tangent tensor fields.
5- Gauss-Codazzi equations. 6- Initial-value problem. 7- Junction
conditions and thin shells. 8- Oppenheimer-Snyder collapse. 9-
Thin-shell collapse. 10- Slowly rotating shell. 11- Null shells.
-
Lagrangian and Hamiltonian formulations of general
relativity
1- Lagrangian formulation. 2- Hamiltonian formulation. 3- Mass
and angular momentum.
-
Black holes
1- Schwarzschild black hole. 2- Reissner-Nordstrom black hole. 3-
Kerr black hole. 4- General properties of black holes. 5- The laws of
black-hole mechanics.
