On the causality of a dilute gas as a dissipative relativistic fluid theory of divergence type

Abstract

The dissipative relativistic fluid theories of divergence type are the simplest theories which are physically consistent and have a well posed-hyperbolic-initial value formulation, since they can be constructed from a single scalar function chi and a dissipation-source tensor Iab, both of them functions of fluid variables. In this work we find the expression for this generating function for the case of a dilute gas using only the knowledge of an equilibrium fluid state, which is known from the kinetic theory of dilute gases. The generating function is obtained by imposing some conditions on the divergence theory, related to the symmetry and trace of the tensor of the fluxes. These conditions come naturally from kinetic theory, and are needed to correctly describe a dilute gas. We prove that in the neighbourhood of the equilibrium states, these divergence type equations for a dilute gas are causal for Boltzmann, Fermi or Bose equilibrium distribution functions.