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String theory and gauge/gravity duality suggest the lower bound of shearviscosity (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 andmu <= 1. Motivated by this, we explore eta/s in black hole accretion flows, inorder to understand if such exotic flows could be a natural site for the lowesteta/s. Accretion flow plays an important role in black hole physics inidentifying the existence of the underlying black hole. This is a rotatingshear flow with insignificant molecular viscosity, which could however have asignificant turbulent viscosity, generating transport, heat and hence entropyin the flow. However, in presence of strong magnetic field, magnetic stressescan help in transporting matter independent of viscosity, via celebratedBlandford-Payne mechanism. In such cases, energy and then entropy produces viaOhmic dissipation. In addition, certain optically thin, hot, accretion flows,of temperature >~ 10^9K, may be favourable for nuclear burning which couldgenerate/absorb huge energy, much higher than that in a star. We find thateta/s in accretion flows appears to be close to the lower bound suggested bytheory, if they are embedded by strong magnetic field or producing nuclearenergy, when the source of energy is not viscous effects. A lower bound oneta/s also leads to an upper bound on the Reynolds number of the flow.

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