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

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

2006-11-08

arxiv.org/abs/gr-qc/0611053v1

Class.Quant.Grav.24:1809-1832,2007

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

34 pages, 18 figures, LaTex

Scientific paper

10.1088/0264-9381/24/7/008

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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