Quasinormal modes in charged fluids at complex momentum

TL;DR

This paper explores the convergence properties of relativistic hydrodynamics in charged fluids using holography, analyzing analyticity, perturbative expansions, and pole-skipping phenomena to understand the limits of hydrodynamic descriptions.

Contribution

It provides a detailed analysis of the convergence radius of hydrodynamic modes in charged fluids and establishes the occurrence of pole-skipping beyond this radius.

Findings

Radius of convergence varies with charge and mode type.

Pole-skipping can occur outside the hydrodynamic convergence radius.

Convergence is finite for neutral fluids but vanishes at extremality.

Abstract

We investigate the convergence of relativistic hydrodynamics in charged fluids, within the framework of holography. On the one hand, we consider the analyticity properties of the dispersion relations of the hydrodynamic modes on the complex frequency and momentum plane and on the other hand, we perform a perturbative expansion of the dispersion relations in small momenta to a very high order. We see that the locations of the branch points extracted using the first approach are in good quantitative agreement with the radius of convergence extracted perturbatively. We see that for different values of the charge, different types of pole collisions set the radius of convergence. The latter turns out to be finite in the neutral case for all hydrodynamic modes, while it goes to zero at extremality for the shear and sound modes. Furthermore, we also establish the phenomenon of pole-skipping for the Reissner-Nordstrom black hole, and we find that the value of the momentum for which this phenomenon occurs need not be within the radius of convergence of hydrodynamics.