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

TL;DR

This paper computes the shear viscosity to entropy density ratio for a 5D Einstein-Yang-Mills black brane using two methods, confirming the universal value in certain limits and discussing discrepancies.

Contribution

It compares Kubo and membrane paradigm methods for calculating viscosity ratio in Einstein-Yang-Mills gravity, highlighting their agreement and differences.

Findings

Kubo method yields 1/4π exactly.

Membrane paradigm approaches 1/4π in large horizon limit.

Discrepancy discussed between the two methods.

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.