Black Brane Viscosity and the Gregory-Laflamme Instability

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.

16 pages, 3 figures. v2: minor corrections and refs added

References in corpus (10)

• Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics
• Nonlinear Fluid Dynamics from Gravity
• Bulk viscosity of gauge theory plasma at strong coupling
• Essentials of Blackfold Dynamics
• Forced Fluid Dynamics from Gravity
• Rayleigh-Plateau and Gregory-Laflamme instabilities of black strings
• New Horizons for Black Holes and Branes
• Black Holes as Lumps of Fluid
• High and Low Dimensions in The Black Hole Negative Mode
• Black hole-black string phase transitions from hydrodynamics

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