TY - JOUR

T1 - Ratio of shear viscosity to entropy density in generalized theories of gravity

AU - Brustein, Ram

AU - Medved, A. J.M.

PY - 2009/1/5

Y1 - 2009/1/5

N2 - Near the horizon of a black brane solution in anti-de Sitter space, the long-wavelength fluctuations of the metric exhibit hydrodynamic behavior. For Einstein's theory, the ratio of the shear viscosity of near-horizon metric fluctuations η to the entropy per unit of transverse volume s is η/s=1/4π. 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 1/4π. Our proposal confirms that η/s is equal to 1/4π 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 η/s. The proposed formula reproduces, in a very simple manner, some recently found results for Gauss-Bonnet gravity. We also make a prediction for η/s in Lovelock theories of any order or dimensionality.

AB - Near the horizon of a black brane solution in anti-de Sitter space, the long-wavelength fluctuations of the metric exhibit hydrodynamic behavior. For Einstein's theory, the ratio of the shear viscosity of near-horizon metric fluctuations η to the entropy per unit of transverse volume s is η/s=1/4π. 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 1/4π. Our proposal confirms that η/s is equal to 1/4π 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 η/s. The proposed formula reproduces, in a very simple manner, some recently found results for Gauss-Bonnet gravity. We also make a prediction for η/s in Lovelock theories of any order or dimensionality.

UR - http://www.scopus.com/inward/record.url?scp=59249090721&partnerID=8YFLogxK

U2 - 10.1103/PhysRevD.79.021901

DO - 10.1103/PhysRevD.79.021901

M3 - Article

AN - SCOPUS:59249090721

VL - 79

JO - Physical Review D - Particles, Fields, Gravitation and Cosmology

JF - Physical Review D - Particles, Fields, Gravitation and Cosmology

SN - 1550-7998

IS - 2

M1 - 021901

ER -