Plane symmetric thin-shell wormholes: solutions and stability

TL;DR

This paper constructs and analyzes the stability of plane symmetric thin-shell wormholes, finding that those made of dark energy or cosmological constant fluids are stable, while phantom energy ones are unstable.

Contribution

It introduces a method to construct and analyze the stability of plane symmetric thin-shell wormholes with various matter contents.

Findings

Dark energy and cosmological constant thin-shell wormholes are stable.

Phantom energy thin-shell wormholes are unstable.

Stability depends on the type of matter fluid used.

Abstract

Using the cut-and-paste procedure, we construct static and dynamic plane symmetric wormholes by surgically grafting together two spacetimes of plane symmetric vacuum solutions with a negative cosmological constant. These plane symmetric wormholes may be viewed as domain walls connecting different universes, having planar topology, and upon compactification of one or two coordinates, cylindrical topology or toroidal topology, respectively. A stability analysis is carried out for the dynamic case by taking into account specific equations of state, and a linearized stability analysis around static solutions is also explored. It is found that thin shell wormholes made of a dark energy fluid or of a cosmological constant fluid are stable, while thin shell wormholes made of phantom energy are unstable.