  We consider the Vlasov-Poisson system with spherical symmetry and an exterior
potential which is induced by a point mass in the center. This system can be
used as a simple model for a newtonian galaxy surrounding a black hole. For
this system, we establish a global existence result for classical solutions
with shell-like initial data, i.e. the support of the density is bounded away
from the point mass singularity. We also prove existence and stability of
stationary solutions which describe static shells, where we use a variational
approach which was established by Y. Guo and G. Rein.
