Relativity and Cosmology II

14756.2035 Summer term 2023

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.

Start: April 3.

In addition, there will be a questions and answers session (in presence) on Wednesdays at 12:00 in room 0.02 (new building).

On June 14, this event will not take place.

Start: April 19.

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

Lectures

Mirrors	Section	Release
	Summary and outlook
	9. Classical Tests of General Relativity 9.1. Gravitational redshift	Apr 3
	9.2. Geodesics in Schwarzschild space-time. I	Apr 5
	9.2. Geodesics in Schwarzschild space-time. II
	9.3. Perihelion motion of Mercury	Apr 12
	9.4. Deflection of light 9.5. Shapiro time delay	Apr 17
	9.6. Geodetic precession	Apr 19
	9.7. Lense–Thirring effect
	10. Differential Geometry II: modern formulation 10.1. Tangent space and tangent vectors 10.2. Differentials and cotangent space 10.3. Tensor algebra and metric	Apr 26
	10.4. The exterior algebra 10.5. Exterior 𝑝-forms	May 3
	10.6. Connections and Cartan equations	May 8
	10.7. Metricity, applications, integration 10.8. Maxwell and Einstein equations	May 10
	11. Relativistic Stars and Black Holes 11.1. Elementary theory of degenerate stars	May 15
	11.2. Interior solution of spherically symmetric stars 11.3. Energy density and binding energy	May 17
	11.4. Geometry of the Schwarzschild solution	May 22
	11.4+. Geometry of the TOV solution 11.5. Charged Black Holes	May 25
	11.6. Rotating Black Holes 11.6.1. Kerr solution	Jun 5
	11.6.2. Geodesics in the Kerr geometry	Jun 7
	11.6.3. Ergosphere 11.6.4. Penrose process	Jun 12
	11.6.5. Remarks on black-hole thermodynamics 11.7. Gravitational collapse to black holes	Jun 14
	11.8. Astrophysical black holes	Jun 19
	12. Foundations of Cosmology 12.1. A brief history of cosmology	Jun 21
	12.2. Structures in the Universe and the Cosmological Principle 12.3. Spaces of constant curvature 12.3.1. Form of the metric	Jun 26
	12.3.2. Geometric realisation of spaces with constant curvature 12.4. Spacetime metric and redshift 12.4.1. Robertson–Walker metric	Jun 28
	12.4.1. Robertson–Walker metric (cont'd) 12.4.2. Cosmological redshift
	12.5. Friedmann–Lemaître equations	Jul 3
	12.6. Distance measures	Jul 5
	12.7. Temporal evolution of the scale factor for Λ = 0	Jul 10
	12.8. Horizons 12.9. Solutions for Λ ≠ 0	Jul 12
	Collection

Exercise classes

Start:	April 20
Time and place:	Exercise class I: 14:00–15:30; room 0.01 (new building) Tutor: Tatevik Vardanyan (tatevik@thp.uni-koeln.de)
	Exercise class II: 16:00–17:30; room 0.01 (new building) Tutor: Mauricio Ortiz Torres (mortizto@smail.uni-koeln.de)

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. The exercises will be discussed on the specified date on the sheet and below. Please show up on April 20 with your solutions of the first exercise sheet 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). Please submit the solutions individually (one solution per student), group submissions are not accepted. Attention: The sheet 5 will be discussed on 7th of June (Wednesday) at 16:00-17:30 (both groups together).

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

Exercise	Release	Submit	Discuss	Remark
Sheet 1	Apr 13, 2023	Apr 20	Apr 27
Sheet 2	Apr 20	Apr 27	May 4	ver 1.01
Sheet 3	Apr 27	May 4	May 11
Sheet 4	May 4	May 11	May 25
Sheet 5	May 11	May 25	Jun 7
Sheet 6	May 25	Jun 7	Jun 15	ver 1.10
Sheet 7	Jun 7	Jun 15	Jun 22
Sheet 8	Jun 15	Jun 22	Jun 29
Sheet 9	Jun 22	Jun 29	Jul 6
Sheet 10	Jun 29	Jul 6	Jul 13

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)