Spherically symmetric linear perturbations of electrically counterpoised dust

TL;DR

This paper analyzes linear perturbations of static, spherically symmetric spacetimes with electrically counterpoised dust, showing that perturbations lead to constant velocity motion and can result in black hole formation.

Contribution

It provides a detailed analysis of perturbation dynamics in electrically counterpoised dust spacetimes, highlighting the conditions for stability and black hole formation.

Findings

Fluid elements move with constant velocities during perturbations

No oscillations or exponential growth in perturbations

Perturbations can lead to black hole formation

Abstract

We consider spherically symmetric linear perturbations of static spherically symmetric spacetimes where the matter content is ellectrically counterpoised dust. We show that the evolution equation for the fluid perturbation implies that the fluid elements move with constant velocities. Therefore there are neither oscillations nor exponential departure from the background solution. We present an explicit example that shows that the perturbation could lead to the formation of a black hole.