Can the viscosity in astrophysical black hole accretion disks be close to its string theory bound?

TL;DR

This paper investigates whether astrophysical black hole accretion disks can have shear viscosity to entropy density ratios close to the fundamental lower bound suggested by string theory, considering effects of magnetic fields and nuclear energy.

Contribution

It explores eta/s in accretion flows, showing they can approach the string theory bound under strong magnetic fields or nuclear energy production, highlighting conditions for minimal viscosity effects.

Findings

eta/s can be close to the theoretical lower bound in certain accretion flows

Strong magnetic fields or nuclear energy production influence eta/s values

Lower eta/s implies an upper limit on the flow's Reynolds number

Abstract

String theory and gauge/gravity duality suggest the lower bound of shear viscosity (eta) to entropy density (s) for any matter to be ~ mu hbar/4pi k_B, when hbar and k_B are reduced Planck and Boltzmann constants respectively and mu <= 1. Motivated by this, we explore eta/s in black hole accretion flows, in order to understand if such exotic flows could be a natural site for the lowest eta/s. Accretion flow plays an important role in black hole physics in identifying the existence of the underlying black hole. This is a rotating shear flow with insignificant molecular viscosity, which could however have a significant turbulent viscosity, generating transport, heat and hence entropy in the flow. However, in presence of strong magnetic field, magnetic stresses can help in transporting matter independent of viscosity, via celebrated Blandford-Payne mechanism. In such cases, energy and then entropy produces via Ohmic dissipation. In addition, certain optically thin, hot, accretion flows, of temperature >~ 10^9K, may be favourable for nuclear burning which could generate/absorb huge energy, much higher than that in a star. We find that eta/s in accretion flows appears to be close to the lower bound suggested by theory, if they are embedded by strong magnetic field or producing nuclear energy, when the source of energy is not viscous effects. A lower bound on eta/s also leads to an upper bound on the Reynolds number of the flow.