Transverse shear viscosity to entropy density for the general anisotropic black brane in Horava–Lifshitz gravity

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 14π\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{{1}}{4\pi }$$\end{document}. The ratio of shear viscosity to entropy density is proportional to the inverse square coupling of quantum thermal field theory, ηs∼1λ2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{{\eta }}{s} \sim \frac{{1}}{\lambda ^2 }$$\end{document}. Especially in QFT with gravity dual the stronger coupling means the shear viscosity per entropy density gets closer to the lower bound of 14π\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{{1}}{4\pi }$$\end{document}. The KSS bound preserves in the anisotropic scaling model.