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 non–barotropic equation of state.