Stable central structures in topologically nontrivial Anti-de Sitter spacetimes

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.