Stable First-order Particle-frame Relativistic Hydrodynamics for Dissipative Systems

TL;DR

This paper introduces a stable first-order relativistic dissipative hydrodynamic equation in the particle frame, derived from the relativistic Boltzmann equation, which could serve as a foundation for more advanced causal theories.

Contribution

The authors present the first stable first-order relativistic dissipative hydrodynamic equation in the particle frame, addressing stability issues of previous models.

Findings

Demonstrated equilibrium stability of the proposed equation

Derived from relativistic Boltzmann equation

Potential basis for second-order causal hydrodynamics

Abstract

We propose a stable first-order relativistic dissipative hydrodynamic equation in the particle frame (Eckart frame) for the first time. The equation to be proposed was in fact previously derived by the authors and a collaborator from the relativistic Boltzmann equation. We demonstrate that the equilibrium state is stable with respect to the time evolution described by our hydrodynamic equation in the particle frame. Our equation may be a proper starting point for constructing second-order causal relativistic hydrodynamics, to replace Eckart's particle-flow theory.