Jürgen Ehlers Spring School

organized by the University of Potsdam and the Max Planck Institute for Gravitational Physics (Albert Einstein Institute)

6. - 17. March 2017

The University of Potsdam and the Max Planck Institute for Gravitational Physics (Albert Einstein Institute) offer a crash course on General Relativity and its astrophysical applications. This course can be attended by European students studying in their 5th semester Physics or Mathematics. The seminar consists of 3 lectures (to be held in English):

  1. Introduction to General Relativity (Axel Kleinschmidt)
  2. Black holes (Hadi Godazgar)
  3. Gravitational Waves (Tanja Hinderer & Jan Steinhoff)


The timetable is arranged to provide two lectures in the morning, each one lasting 120 minutes. In the afternoon there will be opportunities for questions and discussions.

The lectures will take place daily from 9.15 - 10.45 and 11.15 - 12.45 in the lecture hall of the main building of the Max Planck campus in Golm (near Potsdam).

Participants studying outside the area Potsdam-Berlin will be supported financially by 200 Euros. The ‘Fachschaft Physik' of the University of Potsdam will provide assistance in finding accommodation. Information on how to get to the Max Planck campus in Golm can be found here. 


Max Planck Institute for Gravitational Physics
Britta Weihmann
Am Mühlenberg 1
14476 Potsdam-Golm


Via the online registration from 15. November 2016 to 06. January 2017. About the allocation of places will be decided until 13. January.

The number of participants is limited to 40.


1st week: Introduction to general relativity

Starting from a review of special relativity, the lectures will introduce the physical and mathematical concepts needed to formulate and study Einstein's theory of general relativity. Topics include the principle of equivalence, the geometry of curved space-time, introductory concepts of cosmology and basic tests of general relativity.

2nd week: Geometry of black holes

Black holes play a central role in the general theory of relativity, being found within months of Einstein's field equations. The importance of black holes in astrophysics and quantum gravity pertain to the inevitability of their existence, their simplicity and yet their, as yet ununderstood, singularity. In these lectures I will review the Kerr family of rotating solutions and their properties, including their Penrose diagram and maximal analytic extension. Then I will discuss two topics of current interest in black hole research: The quantum properties of black holes (black hole laws of thermodynics and Hawking radiation) and their stability and quasinormal modes.

2nd week: Gravitational waves 

The lecture starts with an overview of gravitational wave astronomy. Several lectures are devoted to discussing the properties, sources, and detectors of gravitational waves. The foundations of data analysis are introduced. Finally, we discuss future prospects and remaining challenges in gravitational wave science.


A working knowledge of freshman physics (classical mechanics, electromagnetism), and mathematics (advanced calculus, linear algebra) will be assumed. Some prior exposure to differential geometry is desirable but not required. 

Complementary Reading

Introduction to the general theory of relativity

  • Schutz, B., A first course in General Relativity
  • Wald, R., General Relativity
  • Weinberg, S., Gravitation and Cosmology


Geometry of black holes

  • Wald, General Relativity, University of Chicago Press, 1984
  • Townsend, B., Black Holes, arXiv:gr-qc/9707012
  • Kokkotas, K., Schmidt, B., Quasi-Normal Modes of Stars and Black Holes, Living Rev. Relativity, 2 (1999) 2


Gravitational waves