Self-similar and charged spheres in the diffusion approximation

TL;DR

This paper presents a new self-similar, charged sphere model in the diffusion approximation, showing how collapse halts with oscillations, transitioning to a static dust configuration.

Contribution

It introduces a simple, physically meaningful self-similar solution for charged spheres that demonstrates a novel collapse behavior with damped oscillations.

Findings

Collapse halts with damped mass oscillations

The model transitions to a static dust configuration

Provides a new analytical solution in the diffusion approximation

Abstract

We study spherical, charged and self--similar distributions of matter in the diffusion approximation. We propose a simple, dynamic but physically meaningful solution. For such a solution we obtain a model in which the distribution becomes static and changes to dust. The collapse is halted with damped mass oscillations about the absolute value of the total charge.