Field redefinition and its impact in relativistic hydrodynamics

TL;DR

This paper investigates how field redefinitions in relativistic hydrodynamics influence the spectrum of perturbations, revealing that non-hydrodynamic modes can be eliminated through redefinition, which affects the physical interpretation of these modes.

Contribution

It demonstrates that non-hydrodynamic modes are artifacts of variable choice and can be removed, clarifying their physical significance in relativistic hydrodynamics.

Findings

Non-hydrodynamic modes are unaffected by local field redefinitions.

All-order redefinition can eliminate non-hydrodynamic modes.

Stress-energy tensor series may have infinite convergence radius linked to non-hydrodynamic modes.

Abstract

In this paper, we explore the impact of field redefinition on the spectrum of linearized perturbations in relativistic hydrodynamics. We observe that the spectrum of hydrodynamics modes is never affected by the local field redefinition, however, the spectrum of the non-hydrodynamic modes is affected. Through an appropriate all-order redefinition, non-hydrodynamic modes can be eliminated, leading to a new frame where the spectrum contains only hydrodynamic modes. We also observe that the resulting stress-energy tensor may have an infinite series in momentum space, with a convergence radius linked to the eliminated non-hydrodynamic mode. In certain special cases, higher-order terms in the stress-energy tensor under field redefinition may cancel, indicating that non-hydrodynamic modes are mere artefacts of the fluid variable choice and hold no physical significance, even if they appear to violate physical constraints. Using a special toy example, we find a criterion to distinguish between physical and unphysical non-hydrodynamic modes.