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, and singularity-free 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 being 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.