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

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.