Stability analysis of dynamic thin shells

TL;DR

This paper investigates the stability of spherically symmetric thin shells, including momentum flux effects, deriving a master equation to identify stable configurations, with applications to black holes and traversable wormholes.

Contribution

It introduces a comprehensive stability analysis incorporating momentum flux, extending previous models, and explores stability regions for wormholes with specific geometric functions.

Findings

Stability regions for thin shells around black holes are consistent with prior results.

Appropriate choices of redshift functions can significantly enhance wormhole stability.

The derived master equation effectively predicts stable equilibrium configurations.

Abstract

We analyze the stability of generic spherically symmetric thin shells to linearized perturbations around static solutions. We include the momentum flux term in the conservation identity, deduced from the ''ADM'' constraint and the Lanczos equations. Following the Ishak-Lake analysis, we deduce a master equation which dictates the stable equilibrium configurations. Considering the transparency condition, we study the stability of thin shells around black holes, showing that our analysis is in agreement with previous results. Applying the analysis to traversable wormhole geometries, by considering specific choices for the form function, we deduce stability regions, and find that the latter may be significantly increased by considering appropriate choices for the redshift function.