Relativity and Cosmology II

14756.2011 (KLIPS / ILIAS)  |  Summer term 2021

Prof. Dr. Claus Kiefer

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

Black hole concept drawing

Lectures

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

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

Further reading

Contents of the lecture
  • 10. Differential geometry II: Modern formulation
  • 11. Relativistic stars and black holes
  • 12. Foundations of Cosmology
  • 13. The Early Universe
  • 14. Quantum Theory and Gravity

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