THEORY OF GENERAL RELATIVITY

Fall 2019

Instructor:
Ana Achúcarro, Oort 269, ext. 5518,
email: achucar (at) lorentz.leidenuniv.nl

Teaching assistants:
Guadalupe Canas Herrera, Oort 272, ext. 5515
email: canasherrera (at) lorentz.leidenuniv.nl
Alexandar Bukva , Oort 238, ext. 5503
email: Bukva (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: Mondays 2pm-4pm (Aleksandar, Oort 238); Wednesdays 9am-11am (Guadalupe, Oort 272). Or by appointment with Ana (Oort 269)

Lectures and werkcolleges in room H207 on Tuesdays 11:15-13:00 and in H106 on Thursdays 14:15-16:00 (please check later for possible room changes). The problem sessions are interactive. The material covered in the problems constitutes an essential part of the programme.

The final exam was on Tuesday 3/12, 10:00 - 13:00, Snellius 407 & 412.

It was a written exam, without books. You could bring a one-page summary of formulas, etc. and a calculator.

The final grades for the course can be found here (revised version). You could check the grading of the final exam on Thursday Dec. 5th from 11:30-12:30 in Ana's office. There wqw a retake exam on 23rd Jan 2020 2:15pm - 5:15 pm in Huygens 211. The grades for the retake can be found here. If you want to check the grading please email us to make an appointment.

Date	Contents (tentative, and optimistic - make sure to check again later). Version revised November 14th.

17/9	Introduction/review of Special Relativity. Schwarzschild radius associated to a spherical mass M. An informal introduction to vectors and parallel transport in manifolds. (C 1.1-1.4) Variational calculation of geodesics.
19/9	Problem set 1
24/9	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	Problem set 2
1/10	Lecture continued
3/10	No class. Leidse Ontzet
8/10	Energy and momentum of a particle. Energy-momentum tensor of a fluid (C 1.9). Conservation of the energy-momentum tensor.
10/10	More mathematics: covariant derivative, Christoffel connection. Parallel transport and geodesics. Geodesic deviation. Curvature. Riemann tensor, Ricci scalar, Einstein tensor. (C 3.2-3.7, 3.10)
15/10	Lecture continued. Problem set 3.
17/10	Lecture moved to 22/10 due to sickness, replaced by problem session. Review of problem sets 1, 2.
22/10	Lecture continued. Energy-momentum tensor. Energy conditions (weak, null, dominant, strong). Einstein equations for the gravitational field. Einstein - Hilbert action (C 4.1-4.7)
24/10	Lecture continued, discussion of problem set 3.
29/10	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 3.8, 2.6, ch 5, ch 8).
31/10	Midterm exam 2pm-4pm (note unusual starting time). It was a closed-book exam. This was also the deadline for handing in two exam questions on the equivalence principle, with solutions, as described in problem set 2. The results of the midterm (up to one bonus point in the final course grade) can be found here.
5/11	Lecture continued and Problem set 4.
7/11	Lecture continued. The metric of charged black holes (Reissner-Nordstrom). Star interiors, Tolman-Oppenheimer-Volkoff equation, gravitational collapse.
12/11	Lecture continued and Problem set 5.
14/11	Review of problem sets 4 and 5. Final review of the course.