Equation of state and transport processes in self-similar spheres

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 nonbarotropic equation of state.