Linearised stability analysis of generic thin shells

TL;DR

This paper develops a comprehensive stability analysis for spherically symmetric thin shells, considering both internal physics and external interactions, with applications to gravastars and wormholes.

Contribution

It provides a general, unified framework for analyzing the stability of thin shells, incorporating internal and external effects in a broad class of spacetimes.

Findings

Stability depends on the properties of the material on the shell.

The analysis applies to gravastars and wormhole geometries.

A general criterion for shell stability is established.

Abstract

We construct generic spherically symmetric thin shells by using the cut-and-paste procedure. We take considerable effort to make the analysis as general and unified as practicable; investigating both the internal physics of the transition layer and its interaction with "external forces" arising due to interactions between the transition layer and the bulk spacetime. We demonstrate in full generality that stability of the thin shell is equivalent to choosing suitable properties for the material residing on the junction interface. Applications to gravastars and wormhole geometries are also explored.