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The Vlasov-Einstein system describes the evolution of an ensemble ofparticles (such as stars in a galaxy, galaxies in a galaxy cluster etc.)interacting only by the gravitational field which they create collectively andwhich obeys Einstein's field equations. The matter distribution is described bythe Vlasov or Liouville equation for a collisionless gas. Recent investigationsseem to indicate that such a matter model is particularly suited in a generalrelativistic setting and may avoid the formation of naked singularities, asopposed to other matter models. In the present note we consider theVlasov-Einstein system in a spherically symmetric setting and prove theexistence of static solutions which are asymptotically flat and have finitetotal mass and finite extension of the matter. Among these there are smooth,singularity-free solutions, which have a regular center and may have isotropicor anisotropic pressure, and solutions, which have a Schwarzschild-singularityat the center. The paper extends previous work, where smooth, globally definedsolutions with regular center and isotropic pressure were considered.Comment: 20 pages, Latex, report #

Static solutions of the spherically symmetric Vlasov–Einstein system