Relativistic fluid dynamics in a 'hydro' frame

TL;DR

This paper explores how field redefinitions affect the spectrum of linearized perturbations in relativistic fluid dynamics, introducing a 'hydro' frame that isolates hydrodynamic modes and clarifies the role of non-hydrodynamic modes in the theory's convergence.

Contribution

It demonstrates that non-hydrodynamic modes can be eliminated via all-order field redefinitions, leading to a new frame containing only hydrodynamic modes and clarifying the convergence properties of the stress-energy tensor.

Findings

Hydrodynamic modes remain unaffected by local field redefinitions.

Non-hydrodynamic modes can be removed through all-order redefinitions.

The stress-energy tensor in the hydro frame may be an infinite series with a convergence radius linked to non-hydrodynamic modes.

Abstract

In this letter, we investigate how field redefinition influences the spectrum of linearized perturbations in relativistic fluid dynamics. We show that the hydrodynamic modes do not get affected under local field redefinition, whereas the non-hydrodynamic modes do. These non-hydrodynamic modes can be removed through a suitable all-order field redefinition. This process leads to a new frame containing only hydrodynamic modes, which we refer to as the hydro frame. Additionally, we demonstrate that the resulting stress-energy tensor may constitute an infinite series in momentum space, with the radius of convergence associated with the removed non-hydrodynamic mode, highlighting its role in the hydrodynamic expansion's validity.