Viscoelastic hydrodynamics of charged black holes

TL;DR

This paper explores the hydrodynamic behavior of charged black holes in AdS space, revealing viscoelastic properties, instabilities driven by higher-form charge fluctuations, and a connection to heat diffusion modes.

Contribution

It demonstrates that perturbations of charged AdS black holes are governed by viscoelastic hydrodynamics and derives a simplified heat diffusion description from this framework.

Findings

Identification of viscoelastic hydrodynamics governing black hole perturbations

Discovery of instabilities driven by higher-form charge fluctuations

Derivation of heat diffusion mode from viscoelastic theory

Abstract

We study the dynamics of an isotropic, planar AdS black hole charged under a pair of two-form gauge potentials. We prove that long wavelength, small amplitude perturbations of this state are governed by the relativistic theory of viscoelastic hydrodynamics. We use this effective theory to identify instabilities in certain regions of parameter space, and show that the dominant instability is always driven by fluctuations of an incoherent density of the higher-form charge. The spacetime we study also arises as a solution to gravity coupled to a pair of massless scalar fields, where part of its dynamics is governed by a simpler effective theory of heat diffusion. We derive this simpler description directly from viscoelastic hydrodynamics, demonstrating that the heat diffusion mode is the collective excitation of the viscoelastic fluid under no-flux boundary conditions.