Implications of a viscosity bound on black hole accretion

TL;DR

This paper investigates the shear viscosity to entropy density ratio in black hole accretion flows, considering different equations of state, and explores implications for primordial black holes and accretion physics.

Contribution

It analyzes eta/s in accretion flows using ideal gas and QCD equations of state, revealing bounds related to black hole mass and accretion conditions.

Findings

eta/s is small only for primordial black holes

eta/s is much larger than known fluids for stellar and supermassive black holes

Lower bounds on black hole mass relate to bounds on eta/s

Abstract

Motivated by the viscosity bound in gauge/gravity duality, we consider the ratio of shear viscosity (eta) to entropy density (s) in black hole accretion flows. We use both an ideal gas equation of state and the QCD equation of state obtained from lattice for the fluid accreting onto a Kerr black hole. The QCD equation of state is considered since the temperature of accreting matter is expected to approach 10^{12}K in certain hot flows. We find that in both the cases eta/s is small only for primordial black holes and several orders of magnitude larger than any known fluid for stellar and supermassive black holes. We show that a lower bound on the mass of primordial black holes leads to a lower bound on eta/s and vice versa. Finally we speculate that the Shakura-Sunyaev viscosity parameter should decrease with increasing density and/or temperatures.