Shear viscosity, instability and the upper bound of the Gauss-Bonnet coupling constant

Xian-Hui Ge, Sang-Jin Sin

Published 2009-03-14, updated 2009-05-16Version 3

We compute the dimensionality dependence of $\eta/s$ for charged black branes with Gauss-Bonnet correction. We find that both causality and stability constrain the value of Gauss-Bonnet coupling constant to be bounded by 1/4 in the infinite dimensionality limit. We further show that higher dimensionality stabilize the gravitational perturbation. The stabilization of the perturbation in higher dimensional space-time is a straightforward consequence of the Gauss-Bonnet coupling constant bound.