Stability of a $d$-dimensional thin-shell wormhole surrounded by quintessence

TL;DR

This paper investigates the stability of higher-dimensional thin-shell wormholes surrounded by quintessence, exploring various throat geometries and their topologies, and providing a comprehensive stability analysis within general relativity.

Contribution

It introduces a generalized stability analysis for higher-dimensional thin-shell wormholes with different geometries, extending previous models to include quintessence and diverse topologies.

Findings

Planar and hyperbolic geometries allow higher-dimensional domain walls or branes.

Stability conditions depend on the geometry and matter content.

The analysis recovers known stability conditions as special cases.

Abstract

We study the stability of different higher dimensional thin--shell wormholes (HDTSW) in general relativity with a cosmological constant. We show that a $d$--dimensional thin--shell wormhole surrounded by quintessence can have three different throat geometries: spherical, planar and hyperbolic. Unlike the spherical geometry, the planar and hyperbolic geometries allow different topologies that can be interpreted as higher-dimensional domain walls or branes connecting two universes. To construct these geometries, we use the cut-and-paste procedure by joining two identical vacuum spacetime solutions. Properties such as the null energy condition and geodesics are also studied. A linear stability analysis around the static solutions is carried out. Our stability analysis takes into account a more general HDTSW geometry than previous works so it is possible to recover other well-known stability HDTSW conditions.