Instructor:
Ana Achúcarro, Oort 269, ext. 5518,
email: achucar (at) lorentz.leidenuniv.nl
Assistant:
Andrey Bagrov, Oort 236, ext. 5513
email: (bagrov (at) lorentz.leidenuniv.nl)
Book:
(C) S. Carroll, Spacetime and Geometry, an Introduction to General
Relativity, Addison-Wesley 2004
Also recommended:
(H) J. Hartle,Gravity, an Introduction to Einstein's General Relativity,
Addison-Wesley 2003
Office hours: to be determined directly with the students
Lectures and werkcolleges: Alternating Mondays or Tuesdays, HL204, 13:45 - 16:30, but there are exceptions (see timetable); Thursdays, HL204, 09:00-10:45 (also with exceptions). The problem sessions are interactive. The material covered in the problems constitutes an essential part of the programme.
| Date | Contents (tentative, and optimistic - make sure to check again later) | |
| 6/9, 15/9 | (no class on 8/9 or 12/9) Introduction/review of Special Relativity. Schwarzschild radius associated to a spherical mass M. An informal introduction to vectors and parallel transport in manifolds. Variational calculation of geodesics. (C 1.1-1.4) | |
| 20/9, 22/9 | Equivalence principle(s). Gravitational time dilation/redshift. Geodesic deviation. Gravity as a metric theory. More mathematics: manifolds, vectors, dual forms, tensors. [Exterior derivative]. (C 1.5-1.7, 2,1-2.5) | |
| 26/9, 29/9 | Energy-momentum tensor of a fluid. Energy conditions (weak, null, dominant, strong). | |
| 4/10, 6/10 | No hoorcollege - replaced by werkcollege. | |
| 10/10, 13/10 | More mathematics: covariant derivative, Christoffel connection. Parallel transport and geodesics. Geodesic deviation. Curvature. Riemann tensor, Ricci scalar, Einstein tensor. (C 1.9, 3.2-3.7, 3.10, 4.6) Einstein equations for the gravitational field. Einstein - Hilbert action (C 3.8, 4.1-4.7) | |
| 18/10, 20/10 | no class | |
| 27/10 | Problem session | |
| 1/11, 3/11 | Symmetries and Killing vectors. Examples. Some important solutions of the Einstein equations. The Schwarzschild metric. The FLRW metric. Cosmological constant and vacuum energy. de Sitter space. (C ch 5, ch 8). | |
| 10/11 | More about black holes (event horizons, causality, Penrose diagrams, black hole thermodynamics). Metric perturbations: gravitational waves, cosmological perturbations. Selected topics from C chapters 6,7,8, depending on available time. |
pdf files with the problems will be downloadable from here
15/9 Problem set 1
22/9 Problem set 2
29/9 Problem set 3
4/10 Extra problem session -- review of sets 1 and 2
6/10 No new problem set - review of set 3
13/10 Problem set 4
20/10 No class
27/10 Problem set 5
3/11 No new problem set. Discussion of energy-momentum tensors.
7/11 Extra problem session
10/11 Problem set 6
28/11 A take-home exam for extra credit is available from Andrey or Ana. It is due on Monday December 19th (three days after the final exam). To get a copy of the exam come to our office, or send us an email in which you state that you understand you are not allowed to communicate with other students about these problems.
The final grades for the course can be found here . Please contact me (by email) if you want to check your grading and/or if you are intending to take the resit exam.