Jürgen Ehlers Spring School

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

7th - 18th March 2016

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 (Cécile Huneau; Jérémie Joudioux)
  2. Black hole space-times (Lars Andersson, Steffen Aksteiner)


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: http://www.aei.mpg.de/48197/01_To_AEI_Potsdam



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


Via the online registration possible from 02.11.2015 to 04.01.2016. About the allocation of places will be decided until 11th January.

The number of participants is limited to 40!


1st week: Introduction to general relativity

The course starts with a review ofNewtonian gravity and special relativitiy. We then discuss the mainprinciples leading to general relativity, and give the background indifferential geometry needed for the formulation of Einstein'sequations. We discuss the properties of some explicit and exactsolutions of Einsteins equations, including the Schwarzschild metric(planetary motion, bending of light, black hole), and the Friedmancosmological models (cosmological redshift, big bang). Finally, we givea brief introduction to gravitational radiation, one of the mostimportant predictions of general relativity.


2nd week: Geometry of black hole spacetimes

Black holes are spacetimes which contain a region from which, due to a strong gravitational field, lightis prevented from escaping. Black holes play a central role inastrophysics, for example most galaxies contain a very massive blackhole at their center. The Kerr spacetime is a solution of the vacuumEinstein equations which describes a stationary, rotating spacetimecontaining a black hole. It is expected to be the unique such spacetime,and is in addition expected to be dynamically stable. In the course wewill discuss some known families of explicit and exact black holesolutions, focussing on the Kerr solution and its properties, includingthe Carter constant, superradiance, Penrose process, particletrajectories and the dynamics of fields in the Kerr spacetime. As partof the course, we shall introduce symbolic computer algebra methodswhich can be used to analyze the geometry of the Kerr spacetime.


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

  1. S. Carroll, Spacetime and Geometry: An Introduction to General Relativity
  2. R.M. Wald, General Relativity (Part I)
  3. J. Stewart, Advanced General Relativity
  4. B.F. Schutz, A First Course in General Relativity
  5. J. Hartle, Gravity: An Introduction to Einstein’s General Relativity