Black Brane Viscosity and the Gregory-Laflamme Instability

TL;DR

This paper connects black brane hydrodynamics with gravitational stability, computing viscosities and analyzing instabilities, and provides a simple approximation for Gregory-Laflamme modes that improves with more dimensions.

Contribution

It extends the blackfold approach by calculating viscosities and linking fluid instabilities to black brane gravitational instabilities, offering a new approximation for the Gregory-Laflamme mode dispersion relation.

Findings

Viscosities saturate generic bounds.

Unstable sound waves relate to Gregory-Laflamme instability.

Approximate dispersion relation improves with more transverse dimensions.

Abstract

We study long wavelength perturbations of neutral black p-branes in asymptotically flat space and show that, as anticipated in the blackfold approach, solutions of the relativistic hydrodynamic equations for an effective p+1-dimensional fluid yield solutions to the vacuum Einstein equations in a derivative expansion. Going beyond the perfect fluid approximation, we compute the effective shear and bulk viscosities of the black brane. The values we obtain saturate generic bounds. Sound waves in the effective fluid are unstable, and have been previously related to the Gregory-Laflamme instability of black p-branes. By including the damping effect of the viscosity in the unstable sound waves, we obtain a remarkably good and simple approximation to the dispersion relation of the Gregory-Laflamme modes, whose accuracy increases with the number of transverse dimensions. We propose an exact limiting form as the number of dimensions tends to infinity.