Causality and stability analysis of first-order field redefinition in relativistic hydrodynamics from kinetic theory

TL;DR

This paper investigates the causality and stability of a first-order relativistic hydrodynamic theory derived from kinetic theory, revealing conditions under which it remains causal and stable, and highlighting methodological considerations.

Contribution

It introduces a systematic approach to analyze causality and stability of first-order relativistic hydrodynamics derived from kinetic theory, emphasizing the importance of background frame considerations.

Findings

Dispersion relations show causality in the local rest frame.

Acausality and instability appear in boosted frames.

Methodological insights for constructing stable first-order theories.

Abstract

In this work, the causality and stability of a first-order relativistic dissipative hydrodynamic theory, that redefines the hydrodynamic fields from a first principle microscopic estimation, have been analyzed. A generic approach of gradient expansion for solving the relativistic transport equation has been adopted using the Chapman-Enskog iterative method. Next, the momentum dependent relaxation time approximation (MDRTA) has been employed to quantify the collision term for analytical estimation of the field correction coefficients from kinetic theory. At linear regime, in local rest frame the dispersion relations are observed to produce a causal propagating mode. However, the acausality and instability reappear when a boosted background is considered for linear analysis. These facts point out relevant aspects regarding the methodology of extracting the causal and stable first order hydrodynamics from kinetic theory and indicate the appropriate approach to construct a valid first order theory with proper justification.