Interaction terms and implementation of the gaseous component

The set of Eqs.(2.22) describe the stellar cluster without taking into consideration the different interaction processes which may play a role in these systems. Heating, cooling processes, mass exchange between stars and gas by stellar mass loss or disruptive stellar collisions, exchange of kinetic internal energy between the stellar system and the interstellar gas via drag forces, loss-cone processes etc are not included in the equations. Here we will give a description for some interesting phenomena that crop up in the systems we want to study. Chapter is partly devoted to a profound description of a loss-cone diffusion model.

In parallel with the description of the interaction terms for the stellar component of a cluster, here we will describe the inclusion of an  in the anisotropic numerical model. For that aim, one should take into account the transfer of radiation in a spherically symmetric moving medium allowing for the contributions which are of the order of the flow velocity divided by the velocity of light, the thermal energy equation and the turbulent energy equation. The equations will be given also ``in their logarithmic form'' (i.e. in our equations we work with $\ln x$ instead of $x$), ready to include in the gaseous model.

The interaction terms for the gaseous component are also described and post-Newtonian corrections are also considered. How these could power the quasar activity by star accretion and energy flows is one of the main questions that could be answered thanks to this method. Therefore we have found of paramount importance to give the set of equations describing this situation.