Entropy production, viscosity bounds and bumpy black holes

The ratio of shear viscosity to entropy density, η/s, is computed in various holographic geometries that break translation invariance (but are isotropic). the shear viscosity does not have a hydrodynamic interpretation in such backgrounds, but does quantify the rate of entropy production due to a strain. fluctuations of the metric components δg xy are massive about these backgrounds, leading to η/s < 1/(4π) at all finite temperatures (even in einstein gravity). as the temperature is taken to zero, different behaviors are possible. if translation symmetry breaking is irrelevant in the far ir, then η/s tends to a constant at t = 0. this constant can be parametrically small. if the translation symmetry is broken in the far ir (which nonetheless develops emergent scale invariance), then η/s ∼ t 2ν as t → 0, with ν ≤ 1 in all cases we have considered. while these results violate simple bounds on η/s, we note that they are consistent with a possible bound on the rate of entropy production due to strain.