The shear diffusion coefficient for generalized theories of gravity

Abstract

Near the horizon of a black brane in Anti-de Sitter (AdS) space and near the AdS boundary, the long-wavelength fluctuations of the metric exhibit hydrodynamic behaviour. The gauge-gravity duality then relates the boundary hydrodynamics for generalized gravity to that of gauge theories with large finite values of 't Hooft coupling. We discuss, for this framework, the hydrodynamics of the shear mode in generalized theories of gravity in d+1 dimensions. It is shown that the shear diffusion coefficients of the near-horizon and boundary hydrodynamics are equal and can be expressed in a form that is purely local to the horizon. We find that the Einstein-theory relation between the shear diffusion coefficient and the shear viscosity to entropy ratio is modified for generalized gravity theories: Both can be explicitly written as the ratio of a pair of polarization-specific gravitational couplings but implicate differently polarized gravitons. Our analysis is restricted to the shear-mode fluctuations for simplicity and clarity; however, our methods can be applied to the hydrodynamics of all gravitational and matter fluctuation modes.

12 pages

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• Shear viscosity and instability from third order Lovelock gravity
• Higher Derivative Corrections to Shear Viscosity from Graviton's Effective Coupling
• Holography of Charged Dilaton Black Holes in General Dimensions
• Hydrodynamics with conserved current via AdS/CFT correspondence in the Maxwell-Gauss-Bonnet gravity
• R^2 Corrections to Asymptotically Lifshitz Spacetimes
• The first order hydrodynamics via AdS/CFT correspondence in the Gauss-Bonnet gravity
• Transport Coefficients from Extremal Gauss-Bonnet Black Holes
• Proof of a universal lower bound on the shear viscosity to entropy density ratio
• Viscosity bound for anisotropic superfluids in higher derivative gravity
• A modulated shear to entropy ratio
• $\eta /s$ at finite coupling
• Unitarity constraints on the ratio of shear viscosity to entropy density in higher derivative gravity
• The sound damping constant for generalized theories of gravity