# Linear Stability Analysis of Evolving Thin Shell Wormholes

## TL;DR

This paper performs a linear stability analysis of dynamic thin shell wormholes using brane world cosmological perturbation theory, revealing conditions under which these wormholes remain stable during evolution.

## Contribution

It introduces a stability analysis for evolving thin shell wormholes constructed via cut-and-paste methods, extending previous static perturbation studies.

## Key findings

- Stable wormholes can be maintained during evolution with appropriate parameters.
- Dynamic wormholes can reach static configurations while remaining stable.
- The analysis complements prior static perturbation work by considering real evolution.

## Abstract

Using ideas from the brane world cosmological perturbation theory, we make linear stability analysis of dynamic thin shell wormholes constructed by cutting-and-pasting two building-block spacetime at arbitrary joining shell radiuses. We observed that in appropriate parameter choices, dynamical thin shell wormholes following from such a cut-and-paste procedure can be kept stable during the whole evolution process towards the final extreme point on which the joining-shell radius arrives on static values. Our work forms a valuable complementarity to previous analysis basing on virtual radial perturbations around the born-static value of the joining-shell radius which allows no real evolution of the wormhole.