On the existence and structure of stationary solutions of the Einstein-Vlasov system

General Relativity, Geometry and Analysis: beyond the first 100 years after Einstein

14 November 10:00 - 11:00

Håkan Andréasson - University of Gothenburg

The present status on the existence and structure of static and stationary solutions of the Einstein-Vlasov system is reviewed. The structure of spherically symmetric static solutions is quite well understood. I will discuss a number of their features, in particular the case of charged solutions since they indicate what properties can be expected of axisymmetric stationary solutions. Existence of axially symmetric stationary solutions that are perturbed off from spherically symmetric Newtonian solutions have been obtained analytically whereas solutions far from being spherically symmetric have only been constructed numerically. I will discuss the properties of the latter. In particular, two different sequences of toroidal solutions which contain ergoregions will be described in detail. These solutions either approach an extreme Kerr black hole or they have the property that the geometry becomes conical in the limit and such solutions may provide models of cosmic strings.
Lars Andersson
Max Planck Institute for Gravitational Physics (Albert Einstein Institute)
Mattias Dahl
KTH Royal Institute of Technology
Philippe G. LeFloch
Sorbonne University
Richard Schoen
University of California, Irvine


Mattias Dahl


For practical matters at the Institute, send an e-mail to