Derivation of transient relativistic fluid dynamics from the Boltzmann equation

TL;DR

This paper derives relativistic fluid dynamics from the Boltzmann equation using a moment method that retains all moments, systematically truncates equations, and relates transport coefficients to microscopic distribution details.

Contribution

It introduces a systematic approach to derive relativistic fluid equations without truncating the distribution function expansion, maintaining all moments and identifying key dynamical variables.

Findings

Equations of motion can be closed with 14 variables up to second order in Knudsen and inverse Reynolds numbers.

Transport coefficients match Chapman-Enskog expansion values.

All moments of the distribution function influence the transport coefficients.

Abstract

In this work we present a general derivation of relativistic fluid dynamics from the Boltzmann equation using the method of moments. The main difference between our approach and the traditional 14-moment approximation is that we will not close the fluid-dynamical equations of motion by truncating the expansion of the distribution function. Instead, we keep all terms in the moment expansion. The reduction of the degrees of freedom is done by identifying the microscopic time scales of the Boltzmann equation and considering only the slowest ones. In addition, the equations of motion for the dissipative quantities are truncated according to a systematic power-counting scheme in Knudsen and inverse Reynolds number. We conclude that the equations of motion can be closed in terms of only 14 dynamical variables, as long as we only keep terms of second order in Knudsen and/or inverse Reynolds number. We show that, even though the equations of motion are closed in terms of these 14 fields, the transport coefficients carry information about all the moments of the distribution function. In this way, we can show that the particle-diffusion and shear-viscosity coefficients agree with the values given by the Chapman-Enskog expansion.