Entropy production, viscosity bounds and bumpy black holes

TL;DR

This paper investigates shear viscosity to entropy density ratio in holographic models with broken translation invariance, revealing violations of simple bounds but consistent with entropy production limits, especially at low temperatures.

Contribution

It provides new insights into how $ta/s$ behaves in non-hydrodynamic, translation-breaking holographic backgrounds, including zero-temperature limits and emergent IR behaviors.

Findings

$ta/s$ is always less than $1/(4\u03c0)$ in these models.

At zero temperature, $ta/s$ approaches a constant or scales as $T^{2 u}$.

Violations of simple $ta/s$ bounds are consistent with entropy production constraints.

Abstract

The ratio of shear viscosity to entropy density, $\eta/s$, 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 $\delta g_{xy}$ are massive about these backgrounds, leading to $\eta/s < 1/(4\pi)$ 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 $\eta/s$ 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 $\eta/s \sim T^{2 \nu}$ as $T \to 0$, with $\nu \leq 1$ in all cases we have considered. While these results violate simple bounds on $\eta/s$, we note that they are consistent with a possible bound on the rate of entropy production due to strain.