Kinetic derivation of nonstationary general relativistic thermodynamics

Abstract

Chernikov, who generalized Grad’s thirteen-moment method for an approximate formal solution of the Boltzmann equation to the case of the general relativistic Boltzmann equation (applicable also to a photon gas), did not exploit his formalism completely but developed the last eight moment equations for dissipation phenomena no further than a stationary theory. However, this stationary theory results in the possibility of the dissipation processes propagating with infinite speed, which is not acceptable. In this paper the complete Chernikov thirteen-moment approximation is developed to obtain nonstationary transport equations, providing linearized collision integrals, for heat and viscous stresses which lead only to finite dissipation speeds. The flux, density and entropy production and therefore the entropy-balance equation representing the second law of thermodynamics is approximated in terms of moments (and microscopic quantities) at the nonstationary level. An expression for entropy production is also deduced as a linear function of the collision integrals. Furthermore, the Gibbs equation, free energy and chemical potential are given in a nonstationary form. A linearized nonstationary heat-conduction equation is derived for a system in mechanical equilibrium without viscous stresses.