# Discontinuity Problem in the Linear Stability Analysis of Thin-Shell Wormholes

## TL;DR

This paper addresses the issue of infinite discontinuities in the stability analysis of thin-shell wormholes by revising the equation of state, successfully eliminating singularities in various wormhole models.

## Contribution

It introduces a method to remove stability diagram singularities through fine-tuning the equation of state at equilibrium.

## Key findings

- Discontinuities in stability diagrams can be eliminated by adjusting the pressure at equilibrium.
- The method is effective for Schwarzschild, extremal Reissner-Nordström, and dilaton thin-shell wormholes.
- Revised equations of state lead to physically acceptable stability analyses.

## Abstract

We investigate the infinite discontinuity points of stability diagram in thin-shell wormholes. The square of the speed of sound $\beta _{0}^{2}$,\ which is expressed in terms of pressure and energy density at equilibrium on the throat, arises with a divergent amplitude. As this is physically non-acceptable, \ we revise the equation of state, such that by fine-tuning of the pressure at static equilibrium, which is at our disposal, eliminates such a singularity. The efficacy of the method is shown in Schwarzschild, extremal Reissner-Nordstr\"{o}m, and dilaton thin-shell wormholes.