Shear Viscosity to Entropy Density for a Black Brane in 5-dimensional Einstein-Yang-Mills Gravity

Abstract

We calculate the ratio of shear viscosity to entropy density for a black brane of $5$-dimensional Einstein-Yang-Mills Gravity by Kubo and membrane paradigm methods. The former gives $\frac{1}{4\pi}$ exactly which is an expected result in the context of the Einstein-Hilbert gravity. In contrast, the membrane paradigm reaches $\frac{1}{4\pi}$ only in large horizon radius limit. We comment on this discrepancy.