PHYS*7840

Advanced General Relativity

Winter 2012

Department of Physics
University of Guelph

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.

Schedule

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.

Textbook

The recommend textbook for the course is

Additional references

Prerequisites

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.

Grading system

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.

Course content

I will select among the following topics, and perhaps insert additional topics as well.

  1. 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.

  2. Geodesic congruences

    1- Energy conditions. 2- Kinematics of a deformable medium. 3- Congruence of timelike geodesics. 4- Congruence of null geodesics.

  3. 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.

  4. Lagrangian and Hamiltonian formulations of general relativity

    1- Lagrangian formulation. 2- Hamiltonian formulation. 3- Mass and angular momentum.

  5. 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.