Third-order relativistic dissipative fluid dynamics from the method of moments

TL;DR

This paper develops a third-order relativistic fluid dynamics theory from the Boltzmann equation, introducing new degrees of freedom and validating it against numerical solutions in a highly symmetric flow scenario.

Contribution

It presents a novel third-order relativistic fluid-dynamical theory derived from the Boltzmann equation, including new tensor degrees of freedom for improved accuracy.

Findings

The theory is linearly causal and stable.

Good agreement with numerical Boltzmann solutions across various parameters.

Abstract

We derive a linearly causal and stable third-order relativistic fluid-dynamical theory from the Boltzmann equation using the method of moments. For this purpose, we demonstrate that such theory must include novel degrees of freedom, corresponding to irreducible tensors of rank 3 and 4. The equations of motion derived in this work are compared with numerical solutions of the Boltzmann equation, considering an ultrarelativistic, classical gas in the highly symmetric Bjorken flow scenario. These solutions are shown to be in good agreement for a wide range of values of shear viscosity and initial temperatures.