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

Ram Brustein, A. J.M. Medved

Research output: Contribution to journalArticlepeer-review

60 Scopus citations


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.

Original languageEnglish
Article number021901
JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
Issue number2
StatePublished - 5 Jan 2009


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