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**Harvard**

Andréasson, H. (2014) *On the existence, structure and stability of static and stationary solutions of the Einstein-Vlasov system*.

** BibTeX **

@conference{

Andréasson2014,

author={Andréasson, Håkan},

title={On the existence, structure and stability of static and stationary solutions of the Einstein-Vlasov system},

booktitle={AIP Conference Proceedings: Plasma Physics and Relativistic Fluids},

isbn={978-0-7354-1208-8},

pages={129-139},

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.},

year={2014},

keywords={Einstein-Vlasov system, Buchdahl inequalities, axially symmetric spacetimes},

}

** RefWorks **

RT Conference Proceedings

SR Electronic

ID 200828

A1 Andréasson, Håkan

T1 On the existence, structure and stability of static and stationary solutions of the Einstein-Vlasov system

YR 2014

T2 AIP Conference Proceedings: Plasma Physics and Relativistic Fluids

SN 978-0-7354-1208-8

SP 129

OP 139

AB 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.

LA eng

DO 10.1063/1.4862458

LK http://dx.doi.org/10.1063/1.4862458

LK http://publications.lib.chalmers.se/records/fulltext/200828/local_200828.pdf

OL 30