Equation of state and transport processes in self--similar spheres

TL;DR

This paper investigates how diffusion and free-streaming transport processes influence the dynamics of collapsing self-similar spheres, revealing stable states with specific equations of state and matching conditions with the Vaidya exterior.

Contribution

It presents a simple self-similar model incorporating transport processes and analyzes the resulting equations of state and stability properties.

Findings

In mixed diffusion and free-streaming cases, a barotropic equation of state emerges in the stationary regime.

Diffusion leads to a constant gravitational potential at the surface.

Perturbed diffusion states tend to recover the barotropic equation of state over time.

Abstract

We study the effect of transport processes (diffusion and free--streaming) on a collapsing spherically symmetric distribution of matter in a self--similar space--time. A very simple solution shows interesting features when it is matched with the Vaidya exterior solution. In the mixed case (diffusion and free--streaming), we find a barotropic equation of state in the stationary regime. In the diffusion approximation the gravitational potential at the surface is always constant; if we perturb the stationary state, the system is very stable, recovering the barotropic equation of state as time progresses. In the free--streaming case the self--similar evolution is stationary but with a non--barotropic equation of state.