On the steady states of the spherically symmetric Einstein-Vlasov system

Abstract

Using both numerical and analytical tools we study various features of static, spherically symmetric solutions of the Einstein-Vlasov system. In particular, we investigate the possible shapes of their mass-energy density and find that they can be multi-peaked, we give numerical evidence and a partial proof for the conjecture that the Buchdahl inequality ${\sup }_{r>0}2m(r)/r<8/9$, $m(r)$ the quasi-local mass, holds for all such steady states--both isotropic {\em and} anisotropic--, and we give numerical evidence and a partial proof for the conjecture that for any given microscopic equation of state--both isotropic {\em and} anisotropic--the resulting one-parameter family of static solutions generates a spiral in the radius-mass diagram.

arXiv comment34 pages, 18 figures, LaTex

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• From Geometry to Numerics: interdisciplinary aspects in mathematical and numerical relativity
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• An introduction to the relativistic kinetic theory on curved spacetimes
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• Accretion of the Vlasov gas on Reissner-Nordström black holes
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