Kinetics of the Compton scattering and the Bose condensation of a photon gas

We study the kinetics of photons coupled to an electron gas by Compton collisions. We show that, for the limiting cases of linear and nonlinear evolutions, an initial narrow spectrum exhibits the same tendency of shifting towards the red frequencies. Concerning the Bose condensation of the photon gas which is predicted by standard thermodynamic arguments when the total number $A$ of photons exceeds some critical value $A_c$, we show that the nonlinear kinetic evolution leads to a condensationlike phenomena. This condensation, which always appears when $A>\mathrm{}{A}_c$, can also occur when $A<\mathrm{}{A}_c$ for sufficiently large and sharply peaked initial photon distributions. Such long-lived quasi-equilibrium states can be called "metastably condensed."