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

Conference paper
Authors Håkan Andreasson
Published in AIP Conference Proceedings: Plasma Physics and Relativistic Fluids
Volume 1578
Pages 129-139
ISBN 978-0-7354-1208-8
ISSN 0094-243X
Publication year 2014
Published at Department of Mathematical Sciences, Mathematics
Pages 129-139
Language en
Links dx.doi.org/10.1063/1.4862458
https://gup.ub.gu.se/file/151811
Keywords Einstein-Vlasov system, Buchdahl inequalities, axially symmetric spacetimes
Subject categories Mathematics, Fusion, Plasma and Space Physics

Abstract

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.

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