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

TL;DR

This paper derives generalized first-order constitutive equations for relativistic fluids by applying the projection method within the Chapman-Enskog expansion, accounting for frame choice and external fields.

Contribution

It introduces a generalized approach to relativistic fluid constitutive equations, explicitly including frame freedom and external electromagnetic influences.

Findings

Derived force-flux relations that are physically consistent for relativistic fluids.

Generalized the first-order correction to include all derivatives of state variables.

Showed special cases lead to physically sound relativistic fluid theories.

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.