Black hole thermodynamics. A classical non-equilibrium approach

The thermodynamic behavior of a black hole, which radiates photons and absorbs energy and matter particles from the surroundings, is given in terms of classical nonequilibrium thermodynamics expressed in the four-dimensional curvilinear coordinates. The local rate of the entropy density change is equal to the divergence of the entropy flow plus a source term. The divergence represents the entropy exchanged between the black hole and the surroundings and accounts for the emission/absorption of photons and the change in composition caused by the matter particles inflow. The entropy source originates from the irreversible processes occurring at the horizon where the infall of energy and matter particles is driven by the gravitational attraction. Considering the given laws of black hole physics, the rate of the entropy change multiplied by T/c(2) gives the rate of mass change. In the frame-work of classical non-equilibrium thermodynamics, the black hole then appears as a system producing entropy during its life, and transforming into entropy, and then into mass, the work done by the gravitational attraction.