Hydro-elastic Complementarity in Black Branes at large D

TL;DR

This paper develops an effective theory describing the non-linear dynamics of black branes at large dimensions, revealing their dual fluid-elastic behavior and analyzing instabilities and perturbations in various spacetime backgrounds.

Contribution

It introduces a unified large-D framework capturing both viscous fluid and elastic membrane descriptions of black branes, extending understanding of their non-linear evolution and stability.

Findings

Black branes behave as viscous fluids and elastic membranes.

The theory describes the non-linear evolution of Gregory-Laflamme instability.

Charged AdS black branes exhibit non-propagating sound modes below a charge-dependent wavelength.

Abstract

We obtain the effective theory for the non-linear dynamics of black branes---both neutral and charged, in asymptotically flat or Anti-deSitter spacetimes---to leading order in the inverse-dimensional expansion. We find that black branes evolve as viscous fluids, but when they settle down they are more naturally viewed as solutions of an elastic soap-bubble theory. The two views are complementary: the same variable is regarded in one case as the energy density of the fluid, in the other as the deformation of the elastic membrane. The large-D theory captures finite-wavelength phenomena beyond the conventional reach of hydrodynamics. For asymptotically flat charged black branes (either Reissner-Nordstrom or p-brane-charged black branes) it yields the non-linear evolution of the Gregory-Laflamme instability at large D and its endpoint at stable non-uniform black branes. For Reissner-Nordstrom AdS black branes we find that sound perturbations do not propagate (have purely imaginary frequency) when their wavelength is below a certain charge-dependent value. We also study the polarization of black branes induced by an external electric field.