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

Hakan Andreasson·Gerhard Rein
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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 $\sup_{r > 0} 2 m(r)/r < 8/9$, $m(r)$ 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.

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Hakan Andreasson, Gerhard Rein. 2006-11-08. On the steady states of the spherically symmetric Einstein-Vlasov system. https://doi.org/10.1088/0264-9381%2F24%2F7%2F008

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