Thermodynamics and bulk viscosity of approximate black hole duals to finite temperature quantum chromodynamics

TL;DR

This paper investigates black hole solutions that mimic QCD thermodynamics to compute bulk viscosity to entropy density ratio, revealing sharp rises near phase transitions and conjecturing links to entropy extrema.

Contribution

It introduces classes of black hole solutions modeling QCD thermodynamics and analyzes their bulk viscosity behavior near phase transitions.

Findings

Sharp rise in zeta/s near T_c for first order transition black holes

Modest increase in zeta/s for smooth cross-over black holes

Divergences in zeta/s linked to entropy density extrema

Abstract

We consider classes of translationally invariant black hole solutions whose equations of state closely resemble that of QCD at zero chemical potential. We use these backgrounds to compute the ratio zeta/s of bulk viscosity to entropy density. For a class of black holes that exhibits a first order transition, we observe a sharp rise in zeta/s near T_c. For constructions that exhibit a smooth cross-over, like QCD does, the rise in zeta/s is more modest. We conjecture that divergences in zeta/s for black hole horizons are related to extrema of the entropy density as a function of temperature.