The ratio of shear viscosity to entropy density in generalized theories of gravity

Abstract

Near the horizon of a black brane solution in Anti-de Sitter space, the long-wavelength fluctuations of the metric exhibit hydrodynamic behaviour. For Einstein's theory, the ratio of the shear viscosity of near-horizon metric fluctuations eta to the entropy per unit of transverse volume s is eta/s=1/4 pi. We propose that, in generalized theories of gravity, this ratio is given by the ratio of two effective gravitational couplings and can be different than 1/4 pi. Our proposal implies that eta/s is equal for any pair of gravity theories that can be transformed into each other by a field redefinition. In particular, the ratio is 1/4 pi for any theory that can be transformed into Einstein's theory; such as F(R) gravity. Our proposal also implies that matter interactions -- except those including explicit or implicit factors of the Riemann tensor -- will not modify eta/s. The proposed formula reproduces, in a very simple manner, some recently found results for Gauss-Bonnet gravity. We also make a prediction for eta/s in Lovelock theories of any order or dimensionality.

11 pages

References in corpus (8)

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• Viscosity, Black Holes, and Quantum Field Theory
• The Lovelock Black Holes
• Universal holographic hydrodynamics at finite coupling
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• The shear viscosity of gauge theory plasma with chemical potentials
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• Second-Order Hydrodynamics and Universality in Non-Conformal Holographic Fluids
• Energy loss of heavy and light quarks in holographic magnetized background
• Hydrodynamics with conserved current via AdS/CFT correspondence in the Maxwell-Gauss-Bonnet gravity
• The shear diffusion coefficient for generalized theories of gravity
• The first order hydrodynamics via AdS/CFT correspondence in the Gauss-Bonnet gravity
• R^2 Corrections to Asymptotically Lifshitz Spacetimes
• A modulated shear to entropy ratio
• Shock waves and Birkhoff's theorem in Lovelock gravity
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• Unitarity constraints on the ratio of shear viscosity to entropy density in higher derivative gravity
• Stringy effects in black hole decay
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• Higher-Curvature Gravity, Black Holes and Holography
• Hydrodynamics dual to Einstein-Gauss-Bonnet gravity: all-order gradient resummation
• Shear viscoelasticity in anisotropic holographic axion model