A Self-Similar Dynamics in Viscous Spheres

We study the evolution of radiating and viscous fluid spheres assuming an additional homothetic symmetry on the spherically symmetric 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.