Relativistic Bose--Einstein condensates thin-shell wormholes

TL;DR

This paper constructs and analyzes the stability of traversable thin-shell wormholes in relativistic Bose-Einstein condensate acoustic metrics, focusing on energy conditions and stability under radial perturbations.

Contribution

It introduces a method to create and examine the stability of relativistic BEC-based wormholes with asymptotic AdS/dS geometries, including energy condition analysis.

Findings

dS acoustic wormholes are stable for small radii

Finite radius wormholes do not violate energy conditions

Large AdS wormholes tend to violate energy conditions and be unstable

Abstract

We construct traversable thin-shell wormholes which are asymptotically Ads/dS applying the cut and paste procedure for the case of an acoustic metric created by a relativistic Bose-Einstein condensate. We examine several definitions of the flare-out condition along with the violation or not of the energy conditions for such relativistic geometries. Under reasonable assumptions about the equation of state of the matter located at the shell, we concentrate on the mechanical stability of wormholes under radial perturbation preserving the original spherical symmetry. To do so, we consider linearized perturbations around static solutions. We obtain that dS acoustic wormholes remain stable under radial perturbations as long as they have small radius, such wormholes with finite radius do not violate the strong/null energy condition. Besides, we show that stable Ads wormhole satisfy some of the energy conditions whereas unstable Ads wormhole with large radii violate them.