Relativity and Cosmology I

14756.2015 (KLIPS / ILIAS)  |  Winter term 2020/21

Prof. Dr. Claus Kiefer

This lecture course will be given in an online format.
Start: Wednesday, Nov 4

A weekly zoom meeting is planned for questions on the course:
Tuesdays, 15:00–15:45
Start: Nov 10
Details have been given by email.

Attention: no zoom meeting on Nov 24, 2020 and Jan 26, 2021.

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

Black hole concept drawing

Lectures

Video organisation: Yi-Fan Wang (yfwang@thp.uni-koeln.de; 3.04 new building)

Mirrors Section Release
Vimeo YouTube 0. Overview Oct 28, 2020
Vimeo YouTube 1. Introduction: A brief history of spacetime Nov 3
Vimeo YouTube 2. Newtonian gravity. I. Nov 4
Vimeo YouTube 2. Newtonian gravity. II. Nov 5
Vimeo YouTube 3. Special relativity
3.1. Poincaré transformation
Nov 6
Vimeo YouTube 3.2. Spacetime diagrams and the relativity of simultaneity Nov 10
Vimeo YouTube 3.3. Time dilation and Lorentz contraction Nov 11
Vimeo YouTube 3.4. Spacetime and four-vectors Nov 12
Vimeo YouTube 3.5. Special relativistic mechanics Nov 17
Vimeo YouTube 4. Gravity as geometry
4.1. The twin problem in special relativity
4.2. Gravitational redshift
Nov 18
Vimeo YouTube 4.3. Motion in a gravitational field Nov 19
Vimeo YouTube 4.4. Newtonian limit (heuristic derivation) Nov 24
Vimeo YouTube 4.5. Curved spaces Nov 25
Vimeo YouTube 5. Differential geometry I: Classic formulation
5.1. Differentiable manifolds
5.2. Vector and tensor fields
5.3. The metric tensor
Dec 1
Vimeo YouTube 5.4. Tensor densities Dec 4
Vimeo YouTube 5.5. Riemann normal coordinates Dec 7
Vimeo YouTube 5.6. Tensor analysis Dec 9
Vimeo YouTube 5.7. The Riemann curvature tensor Dec 16
Vimeo YouTube 5.8. Further discussions of the Riemann tensor
5.9. The Weyl tensor
Dec 18
Vimeo YouTube 5.10. Integration
5.11. Invariant tensor fields and Lie derivatives
Dec 21
Vimeo YouTube 5.12. Killing vectors
5.13. Fermi–Walker transport
Jan 8, 2021
Vimeo YouTube 6. Einstein's field equations and their linear approximation
6.1. The field equations
Jan 11
Vimeo YouTube 6.2. The linear approximation and the Newtonian limit Jan 13
Vimeo YouTube 6.3. Field equations from a variational principle Jan 15
Vimeo YouTube 6.4. Some important examples Jan 20
Vimeo YouTube 6.5. Conservation laws
6.6. General remarks on the structure of the theory
Jan 22
Vimeo YouTube 7. Gravitational waves
7.1. Propagation of gravitational waves
Jan 29
Vimeo YouTube 7.1. Propagation of gravitational waves (cont'd)
7.2. The energy in gravitational wave
Feb 1
Vimeo YouTube 7.3. Emission of gravitational waves Feb 3
Vimeo YouTube 7.3. Emission of gravitational waves (cont'd)
7.4. Detection of gravitational waves
Feb 5
Vimeo YouTube 8. The Schwarzschild solution Feb 8
Vimeo YouTube Summary and outlook Feb 12
Vimeo YouTube Collection

Lecture notes

A script of the lecture notes for the first six chapters can be found here. The password has been 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 with Zoom. Details have been given by email.

Start:

Nov 12

Time and place:   

Exercise class I: 10:00–11:30
Tutor: Tim Schmitz (tschmitz@thp.uni-koeln.de; 107 old building)
Exercise class II: 14:00–15:30
Tutors: Leonardo Chataignier (lcmr@thp.uni-koeln.de; 3.04 new building)

Exercise sheets

New exercise sheets will be released on ILIAS and here below. The solutions can be found on ILIAS.

   Exercise Release Submit Discuss Remark
   Sheet 1 Nov 9, 2020 Nov 16 Nov 19
   Sheet 2 Nov 16 Nov 23 Nov 16
   Sheet 3 Nov 23 Nov 30 Dec 3
   Sheet 4 Nov 30 Dec 7 Dec 10
   Sheet 5 Dec 7 Dec 14 Dec 17
   Sheet 6 Dec 14 Dec 21 Jan 7, 2021
   Sheet 7 Dec 21 Jan 11, 2021 Jan 14
   Sheet 8 Jan 11, 2021 Jan 18 Jan 21 ver 1.02
   Sheet 9 Jan 18 Jan 25 Jan 28
   Sheet 10 Jan 25 Feb 1 Feb 4 ver 1.01
   Sheet 11 Feb 1 Feb 8 Feb 11

Criteria for passing the course

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

Literature

Further reading

Contents of the lecture
  1. Introduction
  2. Newtonian Gravity
  3. Special relativity
  4. Gravity as geometry
  5. Differential geometry I: Classic formulation
  6. Einstein's field equations and their linear approximation
  7. Gravitational waves
  8. The Schwarzschild solution
  9. Geodesics in the Schwarzschild solution

»  Close
Übersichtsplan Physikalische Institute




»  Schließen