Dynamical Instability of Self-Gravitating Membranes

TL;DR

This paper demonstrates that most relativistic membranes with certain physical properties are dynamically unstable, affecting the stability of exotic compact objects like gravastars and wormholes.

Contribution

It provides a general analysis of warping mode instabilities in relativistic membranes and applies the criteria to various exotic compact objects.

Findings

Relativistic membranes with same sign surface density and pressure are unstable.

Gravastars satisfying the weak energy condition are dynamically unstable.

Black hole mimickers are stable only under specific pressure and surface density conditions.

Abstract

We show that a generic relativistic membrane with in-plane pressure and surface density having the same sign is unstable with respect to a series of warping mode instabilities with high wave numbers. We also examine the criteria of instability for commonly studied exotic compact objects with membranes, such as gravastars, AdS bubbles and thin-shell wormholes. For example, a gravastar which satisfies the weak energy condition turns out to be dynamically unstable. A thin-layer black hole mimicker is stable only if it has positive pressure and negative surface density (such as a wormhole), or vice versa.