Abstract
We study electrically charged asymptotically flat black brane solutions whose world-volume fields are slowly varying with the coordinates. Using familiar techniques, we compute the transport coefficients of the fluid dynamic derivative expansion to first order. We show how the shear and bulk viscosities are modified in the presence of electric charge and we compute the charge diffusion constant which is not present for the neutral black p-brane. We compute the first order dispersion relations of the effective fluid. For small values of the charge the speed of sound is found to be imaginary and the brane is thus Gregory-Laflamme unstable as expected. For sufficiently large values of the charge, the sound mode becomes stable, however, in this regime the hydrodynamic mode associated with charge diffusion is found to be unstable. The electrically charged brane is thus found to be (classically) unstable for all values of the charge density in agreement with general thermodynamic arguments. Finally, we show that the shear viscosity to entropy bound is saturated, as expected, while the proposed bounds for the bulk viscosity to entropy can be violated in certain regimes of the charge of the brane.
Highlights
Black branes possess hydrodynamic properties in addition to their thermodynamic properties
We have investigated the nature of the hydrodynamic effective theory that governs the intrinsic long wavelength fluctuations of the Reissner-Nordstrom black brane
Our analysis has extended the established cases of the interrelation between gravity and fluid dynamics
Summary
Black branes possess hydrodynamic properties in addition to their thermodynamic properties. The Maxwell charged black brane solution can straightforwardly be obtained from this family of solutions by specializing to q = 0 and turning off the dilaton coupling This especially means that we can study hydrodynamic fluctuations of pure Einstein gravity coupled to a single gauge field without a dilaton - something which is not possible for generic supergravity backgrounds. We solve the full set of coupled Einstein-Maxwell equations to first order in the derivative expansion and compute the effective stress tensor and current This provides us with the charged generalizations of respectively the shear and bulk viscosity along with the charge diffusion constant which is not present in the neutral case.
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