Transverse Shear Viscosity to Entropy Density for the General Anisotropic Black Brane in Horava-Lifshitz Gravity

Abstract

In this paper we calculate the ratio of transverse shear viscosity to entropy density for the general anisotropic black brane in Horava-Lifshitz gravity. There is a well-known conjecture that states this ratio should be larger than $\frac{1}{4\pi}$. The ratio of shear viscosity to entropy density is proportional to the inverse square coupling of quantum thermal field theory,$\frac{\eta }{s} \sim \frac{1}{\lambda^2 }$. Especially in QFT with gravity dual the stronger coupling means the shear viscosity per entropy density gets closer to the lower bound of $\frac{1}{4\pi}$. The KSS bound preserves in the anisotropic scaling model.