Probing the stability of gravastars by dropping dust shells onto them

TL;DR

This paper investigates the radial stability of gravastars when impacted by dust shells, determining conditions under which they remain stable or convert into black holes, and explores their potential to mimic black holes.

Contribution

It provides a detailed stability analysis of gravastars under dust shell collisions, including generic collision descriptions and numerical results for maximum dust shell mass.

Findings

Most compact gravastars cannot be smaller than typical stars.

Stable gravastars can be pushed beyond the event horizon by dust shells.

Better black hole mimickers are more susceptible to collapse under dust impact.

Abstract

As a preparation for the dynamical investigations, this paper begins with a short review of the three-layer gravastar model with distinguished attention to the structure of the pertinent parameter space of gravastars in equilibrium. Then the radial stability of these types of gravastars is studied by determining their response for the totally inelastic collision of their surface layer with a dust shell. It is assumed that the dominant energy condition holds and the speed of sound does not exceed that of the light in the matter of the surface layer. While in the analytic setup the equation of state is kept to be generic, in the numerical investigations three functionally distinct classes of equations of states are applied. In the corresponding particular cases the maximal mass of the dust shell that may fall onto a gravastar without converting it into a black hole is determined. For those configurations which remain stable the excursion of their radius is assigned. It is found that even the most compact gravastars cannot get beyond the lower limit of the size of conventional stars, provided that the dominant energy condition holds in both cases. It is also shown---independent of any assumption concerning the matter interbridging the internal de Sitter and the external Schwarzschild regions---that the better is a gravastar in mimicking a black hole the easier is to get the system formed by a dust shell and the gravastar beyond the event horizon of the composite system. In addition, a generic description of the totally inelastic collision of spherical shells in spherically symmetric spacetimes is also provided in the appendix.