Short-lived modes from hydrodynamic dispersion relations

TL;DR

This paper demonstrates that hydrodynamic series can be summed to reveal multiple non-hydrodynamic modes, potentially allowing access to the full spectrum of gravitational quasinormal modes from hydrodynamic expansions.

Contribution

It introduces a method to sum hydrodynamic series through branch cuts, uncovering non-hydrodynamic modes from the same series, which is a novel approach.

Findings

Hydrodynamic series can be summed to extend beyond branch cuts.

Multiple non-hydrodynamic modes can be extracted from hydrodynamic series.

The approach suggests full gravitational quasinormal spectra may be accessible from hydrodynamics.

Abstract

We consider the dispersion relation of the shear-diffusion mode in relativistic hydrodynamics, which we generate to high order as a series in spatial momentum q for a holographic model. We demonstrate that the hydrodynamic series can be summed in a way that extends through branch cuts present in the complex q plane, resulting in the accurate description of multiple sheets. Each additional sheet corresponds to the dispersion relation of a different non-hydrodynamic mode. As an example we extract the frequencies of a pair of oscillatory non-hydrodynamic black hole quasinormal modes from the hydrodynamic series. The analytic structure of this model points to the possibility that the complete spectrum of gravitational quasinormal modes may be accessible from the hydrodynamic derivative expansion.