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

TL;DR

This paper proposes a generalized formula for the shear viscosity to entropy density ratio in various gravity theories, extending the well-known Einstein result and predicting values for Lovelock theories.

Contribution

It introduces a new formula linking eta/s to effective gravitational couplings, applicable to a broad class of generalized gravity theories.

Findings

eta/s equals 1/4 pi for Einstein and theories transformable into Einstein's

The formula reproduces known results for Gauss-Bonnet gravity

Predicts eta/s in Lovelock theories of any order or dimension

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.