ar X iv : g r - qc / 0 50 80 54 v 1 1 2 A ug 2 00 5 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.