Relativistic transfer equations: maximum principle and convergence to the non-equilibrium regime

We consider the relativistic transfer equations for photons interacting via emission absorp-tion and scattering with a moving fluid. We prove a minimum-maximum principle and we study the non equilibrium regime: the relativistic correction terms in the scattering operator lead to a frequency drift term modeling the Doppler effects. We prove that the solution of the relativistic transfer equations converges toward the solution of this drift diffusion equation