H-theorem for a relativistic plasma around black holes

A statistical description of matter, formed by a relativistic plasma infalling into a black hole, is formulated, adopting a covariant kinetic approach in terms of classical point particles. By assuming that the charged particles are described by the collisionless Vlasov equation and the event horizon can be treated as a classical porous wall, the theory permits us to evaluate the entropy production rate of classical matter in the presence of an event horizon. As a result, an H-theorem is established for the classical (Shannon) kinetic entropy of the infalling matter, which holds for arbitrary models of black holes and is valid also in the presence of contracting (or expanding) event horizons.