Spherically symmetric electrically counterpoised dust either collapses or disperses

TL;DR

This paper demonstrates that spherically symmetric electrically counterpoised dust either collapses into an extremal Reissner-Nordström black hole or disperses, challenging the idea of neutral equilibrium states as black hole mimickers.

Contribution

It shows that any initial velocity causes these dust configurations to evolve into black holes or disperse, refuting their supposed equilibrium state.

Findings

Small velocities lead to collapse or dispersion.

Collapsed objects are extremal Reissner-Nordström black holes.

Electrically counterpoised dust cannot remain in neutral equilibrium.

Abstract

We explore the dynamical evolution of spherically symmetric objects made of electrically counterpoised dust in general relativity. It has been claimed that these objects are in neutral equilibrium and, therefore, that black hole mimickers made of electrically counterpoised dust are feasible. Here we show that if a velocity is imparted to the fluid elements, no matter how small, the evolution leads either to a black hole or to the dispersion of the fluid. Furthermore, in the case of collapse, the resulting object is necessarily an extremal Reissner-Nordstr\"om black hole.