# Causal Relativistic Hydrodynamics of Conformal Fermi-Dirac Gases

## TL;DR

This paper derives a causal relativistic hydrodynamics framework for Fermi-Dirac gases from kinetic theory, addressing divergence issues and analyzing stability of anisotropic configurations.

## Contribution

It introduces a divergence type theory approach for Fermi-Dirac gases, providing a stable hydrodynamic description contrasting with Grad approximation predictions.

## Key findings

- The derived hydrodynamics are stable for anisotropic configurations.
- Divergence type theories regularize formal divergences in kinetic expressions.
- Hydrodynamics from DTTs differ from Grad approximation in stability predictions.

## Abstract

In this paper we address the derivation of causal relativistic hydrodynamics, formulated within the framework of Divergence Type Theories (DTTs), from kinetic theory for spinless particles obeying Fermi-Dirac statistics. The approach leads to expressions for the particle current and energy momentum tensor that are formally divergent, but may be given meaning through a process of regularization and renormalization. We demonstrate the procedure through an analysis of the stability of an homogeneous anisotropic configuration. In the DTT framework, as in kinetic theory, these configurations are stable. By contrast, hydrodynamics as derived from the Grad approximation would predict that highly anisotropic configurations are unstable.