Relativity and Cosmology II

14756.2011 (KLIPS / ILIAS) | Summer term 2021

This lecture course will be given in an online format.
Start: Monday, Apr 12.

A weekly zoom meeting is planned for questions on the course:
Tuesdays, 15:00–15:45.
Start: Apr 27.
Details will be given by email.

Attention: no zoom meeting on Jun 8 and 15, 2021.

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

Lectures

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

Mirrors	Section	Release
	Summary and outlook	Feb 12
	9. Classical Tests of General Relativity 9.1. Gravitational redshift	Apr 12
	9.2. Geodesics in Schwarzschild space-time. I	Apr 14
	9.2. Geodesics in Schwarzschild space-time. II	Apr 19
	9.3. Perihelion motion of Mercury	Apr 21
	9.4. Deflection of light 9.5. Shapiro time delay	Apr 26
	9.6. Geodetic precession	Apr 28
	9.7. Lense–Thirring effect	May 3
	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	May 7
	10.4. The exterior algebra 10.5. Exterior 𝑝-forms	May 10
	10.6. Connections and Cartan equations	May 12
	10.7. Metricity, applications, integration 10.8. Maxwell and Einstein equations	May 17
	11. Relativistic Stars and Black Holes 11.1. Elementary theory of degenerate stars	May 19
	11.2. Interior solution of spherically symmetric stars 11.3. Energy density and binding energy	May 31
	11.4. Geometry of the Schwarzschild solution	Jun 2
	11.4+. Geometry of the TOV solution 11.5. Charged Black Holes	Jun 7
	11.6. Rotating Black Holes 11.6.1. Kerr solution	Jun 11
	11.6.2. Geodesics in the Kerr geometry	Jun 14
	11.6.3. Ergosphere 11.6.4. Penrose process	Jun 16
	11.6.5. Remarks on black-hole thermodynamics 11.7. Gravitational collapse to black holes	Jun 21
	11.8. Astrophysical black holes	Jun 25
	12. Foundations of Cosmology 12.1. A brief history of cosmology	Jun 28
	12.2. Structures in the Universe and the Cosmological Principle 12.3. Spaces of constant curvature 12.3.1. Form of the metric	Jul 5
	12.3.2. Geometric realisation of spaces with constant curvature 12.4. Spacetime metric and redshift 12.4.1. Robertson–Walker metric	Jul 7
	12.4.1. Robertson–Walker metric (cont'd) 12.4.2. Cosmological redshift	Jul 12
	12.5. Friedmann–Lemaître equations	Jul 14
	12.6. Distance measures	Jul 21
	12.7. Temporal evolution of the scale factor for Λ = 0	Jul 23
	12.8. Horizons 12.9. Solutions for Λ ≠ 0	Jul 26
	Collection

Exercise class

Exercise class will be given on Thursdays with Zoom. Details have been given by email.

Start:	Apr 22
Time and place:	Exercise class I: 14:00 Tutors: Tim Schmitz (tschmitz@thp.uni-koeln.de; 107 old building) Tatevik Vardanyan (tatevik@thp.uni-koeln.de; 107 old 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	Apr 19, 2021	Apr 26	Apr 29
Sheet 2	Apr 26	May 3	May 6	ver 1.01
Sheet 3	May 3	May 10	May 13
Sheet 4	May 10	May 17	May 21
Sheet 5	May 17	May 31	Jun 4
Sheet 6	May 31	Jun 7	Jun 10	ver 1.10
Sheet 7	Jun 7	Jun 14	Jun 17
Sheet 8	Jun 14	Jun 21	Jun 24
Sheet 9	Jun 21	Jun 28	Jul 1
Sheet 10	Jun 28	Jul 5	Jul 8
Sheet 11	Jul 5	Jul 12	Jul 15
Sheet 12	Jul 12	Jul 19	Jul 22

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)