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 massenergy 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 and anisotropic—, and we give numerical evidence and a partial proof for the conjecture that for any given microscopic equation of state—both isotropic and anisotropic— the resulting one-parameter family of static solutions generates a spiral in the radius-mass diagram.