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

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 $\sup_{r > 0} 2 m®/r < 8/9$,$m®$ 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.