On the existence, structure and stability of static and stationary solutions of the Einstein-Vlasov system
Paper in proceedings, 2014

The present status on the existence, structure and stability of static and stationary solutions of the Einstein-Vlasov system is reviewed. Under the assumptions that a spherically symmetric static object has isotropic pressure and non-increasing energy density outwards, Buchdahl showed 1959 the bound M/R<4/9, where M is the ADM mass and R the outer radius. Most static solutions of the Einstein-Vlasov system do not satisfy these assumptions. The bound M/R<4/9 nevertheless holds and it is sharp. An analogous bound in the charged case is also given. The important question of stability of spherically symmetric static solutions is presently open but numerical results are available and these are reviewed. A natural question is to go beyond spherical symmetry and consider axially symmetric solutions, and a recent result on the existence of axially symmetric stationary solutions is also discussed.

axially symmetric spacetimes

Einstein-Vlasov system

Buchdahl inequalities

Author

Håkan Andreasson

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

AIP Conference Proceedings

0094-243X (ISSN) 1551-7616 (eISSN)

Vol. 1578 129-139

Subject Categories

Mathematics

Fusion, Plasma and Space Physics

DOI

10.1063/1.4862458

ISBN

978-0-7354-1208-8

More information

Created

10/7/2017