  The Vlasov-Einstein system describes the evolution of an ensemble of
particles (such as stars in a galaxy, galaxies in a galaxy cluster etc.)
interacting only by the gravitational field which they create collectively and
which obeys Einstein's field equations. The matter distribution is described by
the Vlasov or Liouville equation for a collisionless gas. Recent investigations
seem to indicate that such a matter model is particularly suited in a general
relativistic setting and may avoid the formation of naked singularities, as
opposed to other matter models. In the present note we consider the
Vlasov-Einstein system in a spherically symmetric setting and prove the
existence of static solutions which are asymptotically flat and have finite
total mass and finite extension of the matter. Among these there are smooth,
singularity-free solutions, which have a regular center and may have isotropic
or anisotropic pressure, and solutions, which have a Schwarzschild-singularity
at the center. The paper extends previous work, where smooth, globally defined
solutions with regular center and isotropic pressure were considered.
