Shear hydrodynamics, momentum relaxation, and the KSS bound

In this paper we investigate the behavior of the shear hydrodynamic response functions in a simple holographic model exhibiting momentum relaxation. We compute several stress tensor response functions in the transverse channel, and from there derive the ratio of shear viscosity to entropy density, $\eta/s$, using two different methods. The two values differ from each other, one which satisfies the KSS bound $\eta/s \geq \frac{1}{4\pi}$ and one which does not, and we discuss the causes and implications of this result.