ON THE CAUSALITY OF A DILUTE GAS AS A DISSIPATIVE RELATIVISTIC FLUID THEORY OF DIVERGENCE TYPE

The dissipative relativistic fluid theories of divergence type are the simplest theories which are physically consistent and have a well pos ed-hyperbolic-initial value formulation, since they can be constructed from a single scalar function chi and a dissipation-source tensor I-a b, 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 o btained by imposing some conditions on the divergence theory, related to the symmetry and trace of the tenser of the fluxes. These condition s come naturally from kinetic theory, and are needed to correctly desc ribe a dilute gas. We prove that in the neighbourhood of the equilibri um states, these divergence type equations for a dilute gas are causal for Boltzmann, Fermi or Bose equilibrium distribution functions.