Spherically symmetric linear perturbations of electrically counterpoised dust

Abstract

We consider spherically symmetric linear perturbations of static spherically symmetric spacetimes where the matter content is electrically 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 showing that the perturbation could lead to the formation of a black hole.