First-order general constitutive equations for relativistic fluids using the projection method in the Chapman-Enskog expansion of the Boltzmann equation

Abstract

The first-order out of equilibrium correction to the distribution function, obtained by implementing the projection method for the perturbed relativistic Boltzmann equation using the Chapman-Enskog method, is generalized in order to explicitly include the freedom of choice for frame and representation. It is shown how this procedure leads to general constitutive equations that couple the dissipative fluxes to all derivatives of the state variables (forces), including a weak external electromagnetic field. Special cases of the resulting force-flux relations have been shown to lead to physically sound theories for relativistic fluids.