Linearized stability analysis of thin-shell wormholes with a cosmological constant

TL;DR

This paper analyzes the stability of thin-shell wormholes with a cosmological constant, showing how positive and negative values affect stability regions and energy conditions, using a linearized perturbation approach.

Contribution

It extends stability analysis of thin-shell wormholes to include the effects of a cosmological constant, providing new insights into their stability and energy conditions.

Findings

Positive cosmological constant increases stability regions.

Negative cosmological constant decreases stability regions.

Energy conditions vary with the cosmological constant and throat radius.

Abstract

Spherically symmetric thin-shell wormholes in the presence of a cosmological constant are constructed applying the cut-and-paste technique implemented by Visser. Using the Darmois-Israel formalism the surface stresses, which are concentrated at the wormhole throat, are determined. This construction allows one to apply a dynamical analysis to the throat, considering linearized radial perturbations around static solutions. For a large positive cosmological constant, i.e., for the Schwarzschild-de Sitter solution, the region of stability is significantly increased, relatively to the null cosmological constant case, analyzed by Poisson and Visser. With a negative cosmological constant, i.e., the Schwarzschild-anti de Sitter solution, the region of stability is decreased. In particular, considering static solutions with a generic cosmological constant, the weak and dominant energy conditions are violated, while for $a_0 \leq 3M$ the null and strong energy conditions are satisfied. The surface pressure of the static solution is strictly positive for the Schwarzschild and Schwarzschild-anti de Sitter spacetimes, but takes negative values, assuming a surface tension in the Schwarzschild-de Sitter solution, for high values of the cosmological constant and the wormhole throat radius.