# Håkan Andreasson: On the existence and structure of stationary solutions of the Einstein-Vlasov system

**Time: **
Thu 2019-11-14 10.00 - 11.00

**Location: **
Seminar Hall Kuskvillan, Institut Mittag-Leffler

**Participating: **
Håkan Andreasson, Chalmers/University of Gothenburg

### Abstract

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.