Relativity and Cosmology I

14756.2015 Winter term 2022/23

This course will be given in a hybrid format. The lectures are available online here. For convenience we will republish the material on this page weekly on Monday and Wednesday.

In addition, there will be a weekly zoom meeting for questions and discussions. This is planned for Wednesdays 14:00-15:30, start October 18. Details will be given by e-mail.

Master core course within the Primary Area of Specialization GR-QFT

Lectures

Thanks

Mirrors	Section	Release
	0. Overview	Sep 12, 2022
	1. Introduction: A brief history of spacetime	Oct 10
	2. Newtonian gravity. I.
	2. Newtonian gravity. II.	Oct 12
	3. Special relativity 3.1. Poincaré transformation
	3.2. Spacetime diagrams and the relativity of simultaneity	Oct 17
	3.3. Time dilation and Lorentz contraction
	3.4. Spacetime and four-vectors	Oct 19
	3.5. Special relativistic mechanics
	4. Gravity as geometry 4.1. The twin problem in special relativity 4.2. Gravitational redshift
	4.3. Motion in a gravitational field	Oct 26
	4.4. Newtonian limit (heuristic derivation)
	4.5. Curved spaces
	5. Differential geometry I: Classic formulation 5.1. Differentiable manifolds 5.2. Vector and tensor fields 5.3. The metric tensor	Nov 2
	5.4. Tensor densities
	5.5. Riemann normal coordinates	Nov 7
	5.6. Tensor analysis
	5.7. The Riemann curvature tensor	Nov 9
	5.8. Further discussions of the Riemann tensor 5.9. The Weyl tensor
	5.10. Integration 5.11. Invariant tensor fields and Lie derivatives	Nov 16
	5.12. Killing vectors 5.13. Fermi–Walker transport	Nov 21
	6. Einstein's field equations and their linear approximation 6.1. The field equations	Nov 28
	6.2. The linear approximation and the Newtonian limit	Dec 5
	6.3. Field equations from a variational principle	Dec 7
	6.4. Some important examples	Dec 12
	6.5. Conservation laws 6.6. General remarks on the structure of the theory	Dec 21
	7. Gravitational waves 7.1. Propagation of gravitational waves	Jan 10
	7.1. Propagation of gravitational waves (cont'd) 7.2. The energy in gravitational wave	Jan 12
	7.3. Emission of gravitational waves	Jan 16
	7.3. Emission of gravitational waves (cont'd) 7.4. Detection of gravitational waves	Jan 18
	8. The Schwarzschild solution	Jan 23
	Summary and outlook	Jan 25

Lecture notes

A script of the lecture notes for the first six chapters can be found here. The password will be sent by email.
Script is under construction; additional sections will be added as soon as they are available.

Exercise classes

Exercise classes will be given on Thursdays. Please show up on October 20 at the time of your choice (14:00 or 16:00). Perhaps we have to redistribute the participants in case that too many people have chosen one class (and too little the other classes). For those of you who haven't attended this week's class, please join the second group (16:00) as there are free spots there.

The solutions of the exercise sheets can be found here. The password will be sent by email.

Start:	Oct 20
Time and place:	Exercise class I: 14:00–15:30; Tutor: Tatevik Vardanyan (tatevik@thp.uni-koeln.de); seminar room (old building)
	Exercise class II: 16:00–17:30; Tutor: Mauricio Ortiz Torres (mortizto@smail.uni-koeln.de); seminar room (old building)
	Exercise class III: 14:00–15:30 Tutor: Blanca Hergueta (bherguet@smail.uni-koeln.de); room 0.02 (new building)

Exercise sheets

New exercise sheets will be released each Thursday and can be downloaded below. The exercises have to be submitted one week later in the class (one solution sheet per a group of up to two students). The exercises will be discussed on the specified date on the sheet and below.

Exercise	Release	Submit	Discuss	Remark
Sheet 1	Oct 20, 2022	Oct 27	Nov 3
Sheet 2	Oct 27	Nov 3	Nov 10
Sheet 3	Nov 3	Nov 10	Nov 17
Sheet 4	Nov 10	Nov 17	Nov 24
Sheet 5	Nov 17	Nov 24	Dec 1
Sheet 6	Nov 24	Dec 1	Dec 8
Sheet 7	Dec 1	Dec 8	Dec 15
Sheet 8	Dec 8	Dec 15	Jan 12, 2023	ver 1.02
Sheet 9	Dec 15	Jan 12	Jan 19
Sheet 10	Jan 12	Jan 19	Jan 26	ver 1.01
Sheet 11	Jan 19	Jan 26	Feb 2

Criteria for passing the course

Active participation in the exercise class.
At least 50 % of the credit points from the exercises.

Literature

S. Carroll, Spacetime and Geometry: An Introduction to General Relativity (Addison-Wesley)
The lecture notes, on which this book is based, can be found on arXiv:gr-qc/9712019, and in html at Caltech
J. B. Hartle, Gravity (Addison-Wesley)
S. Carlip, General Relativity, A Concise Introduction (Oxford University Press 2019)