A self-similar dynamics in viscous spheres

TL;DR

This paper investigates self-similar collapse dynamics of viscous, radiating fluid spheres under homothetic symmetry, deriving a simplified model that exhibits physically acceptable behavior and shear-free evolution.

Contribution

It introduces a new self-similar model for viscous spheres with homothetic symmetry, linking interior solutions with Vaidya exterior and analyzing their dynamics.

Findings

Derived a system of two ODEs governing the collapse

Found a shear-free, barotropic self-similar solution

Identified initial conditions leading to physically acceptable evolution

Abstract

We study the evolution of radiating and viscous fluid spheres assuming an additional homothetic symmetry on the spherically simmetric space--time. We match a very simple solution to the symmetry equations with the exterior one (Vaidya). We then obtain a system of two ordinary differential equations which rule the dynamics, and find a self--similar collapse which is shear--free and with a barotropic equation of state. Considering a huge set of initial self--similar dynamics states, we work out a model with an acceptable physical behavior.