Near-horizon analysis of η/s

It is now well understood that the coefficient of shear viscosity of boundary fluid can be obtained from the horizon values of the effective coupling of transverse graviton in bulk spacetime. In this paper we observe that to find the shear-viscosity coefficient it is sufficient to know only the near-horizon geometry of the black hole spacetime. One does not need to know the full analytic solution. We consider several examples including non-trivial matter (dilaton, gauge fields) coupled to gravity in presence of higher derivative terms and calculate shear viscosity for both extremal and non-extremal black holes only studying the near-horizon geometry. In particular, we consider higher derivative corrections to extremal R-charged black holes and compute η/s in presence of three independent charges. We also consider asymptotically Lifshitz spacetime whose dual black hole geometry cannot be found analytically. We study the near horizon behaviour of these black holes and find η/s for its dual plasma at Lifshitz fixed point.