  We investigate stable central structures in multiply-connected, anti de
Sitter spacetimes with spherical, planar and hyperbolic geometries. We obtain
an exact solution for the pressure in terms of the radius when the density is
constant. We find that, apart from the usual simply-connected spherically
symmetric star with a well-behaved metric at $r=0$, the only solutions with
non-singular pressure and density have a wormhole topology. However these
wormhole solutions must be composed of matter which violates the weak energy
condition. Admitting this type of matter, we obtain a structure which is
maintained via a balance between its cohesive tension and its repulsive
negative matter density. If the tension is insufficiently large, this structure
can collapse to a black hole of negative mass.
