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General Relativity (Summer 2019)


Course description

This is an introductory course on the mathematics of special and general relativity. The course is taught by Prof. Karsten Große Brauckmann, and I am responsible for the exercise sessions. Both the lectures and exercise sessions are in English.

Contents will include:

  1. Special relativity and setup for general relativity
  2. Einstein equations
  3. Special solutions and blackholes: Schwarzschild, Kerr, etc.
  4. Further topics: cosmology, gravitational waves...


  1. Differentiable manifolds
  2. Semi-Riemannian metrics
  3. Levi-Civita connection
  4. Geodesics and exponential map
  5. Curvature (Riemann, Ricci, scalar) and geodesics


The main reference we will use is Semi-Riemannian Geometry With Applications to Relativity by Barret O'Neill.

Other references include:

Physics books:

  1. General Relativity by Straumann
  2. Introducing Einstein's Relativity by d'Inverno

Classical physics texts:

  1. Gravitation by Misner, Thorne, Wheeler
  2. The Large Scale Structure of Space-Time by Hawking, Ellis

Math books:

  1. Differentialgeometrie by Kühnel
  2. Einstein manifolds by Besse


Refer to the information sheet on Tucan.

Class time and location & Office hours

Lectures: Fridays 15:20-17:00, room ?
Exercise sessions: Tuesdays 15:20-17:00 (every other week), room S15|301
Office hours: By appointment

NB: Refer to the course schedule below for the precise dates.

Exercise sheets

Click on the exercise sheets below to view or download.

Course schedule

NB: The course schedule below is subject to updates.

Date Subject Remarks
Tuesday 16.04.2019 Lecture #1
Tuesday 23.04.2019 Review session (exceptional)
Friday 26.04.2019 Lecture #2
Tuesday 30.04.2019 Exercise session #1
Friday 03.05.2019 Lecture #3
Friday 10.05.2019 Lecture #4
Tuesday 14.05.2019 Exercise session #2
Friday 17.05.2019 Lecture #5
Friday 24.05.2019 Lecture #6
Tuesday 28.05.2019 Exercise session #3
Friday 31.05.2019 Lecture #7
Friday 07.06.2019 Lecture #8 Cancelled!
Friday 14.06.2019 Lecture #9
Friday 21.06.2019 Lecture #10
Tuesday 25.06.2019 Exercise session #4
Friday 28.06.2019 Lecture #11
Friday 05.07.2019 Lecture #12
Tuesday 09.07.2019 Exercise session #5
Friday 12.07.2019 Lecture #13
Tuesday 16.07.2019
Exercise session #6
Friday 19.07.2019 Lecture #14

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