Field redefinition and its impact in relativistic hydrodynamics

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 nonhydrodynamic modes is affected. Through an appropriate all-order redefinition, nonhydrodynamic 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 nonhydrodynamic mode. In certain special cases, higher-order terms in the stress-energy tensor under field redefinition may cancel, indicating that nonhydrodynamic modes are mere artifacts 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 nonhydrodynamic modes.