Stable central structures in topologically nontrivial Anti-de Sitter spacetimes

TL;DR

This paper explores stable, non-singular central structures in multiply-connected Anti-de Sitter spacetimes, revealing wormhole solutions requiring exotic matter that balances tension and negative density, with potential collapse to negative mass black holes.

Contribution

It provides exact solutions for pressure in constant density Anti-de Sitter spacetimes and identifies novel wormhole structures with unique stability properties.

Findings

Wormhole solutions require matter violating the weak energy condition.

Stable structures balance tension and negative matter density.

Insufficient tension leads to collapse into negative mass black holes.

Abstract

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.