A maximum for the entropy of the relativistic gas in the stationary space-time (Q1090577)

A relativistic gas evolving within a stationary space-time is studied, which is characterized by a privileged direction in time given by the trajectories of the Killing vector. Starting from the distribution function which obeys the relativistic Boltzmann equation, the behaviour of this function in a stationary space-time is investigated, basically in looking for a function which maximizes entropy. This is achieved by regarding entropy as an operator. The explicit evaluation of the maximizing function leads to a Maxwellian.