Hydrodynamics and viscosity in the Rindler spacetime

Abstract

In the past year it has been shown that one can construct an approximate (d + 2) dimensional solution of the vacuum Einstein equations dual to a (d + 1) dimensional fluid satisfying the Navier-Stokes equations. The construction proceeds by perturbing the flat Rindler metric, subject to the boundary conditions of a non-singular causal horizon in the interior and a fixed induced metric on a given timelike surface r = rc in the bulk. We review this fluid-Rindler correspondence and show that the shear viscosity to entropy density ratio of the fluid on r = rc takes the universal value 1/4π both in Einstein gravity and in a wide class of higher curvature generalizations. Since the precise holographic duality for this spacetime is unknown, we propose a microscopic explanation for this viscosity based on the peculiar properties of quantum entanglement. Using a novel holographic Kubo formula in terms of a two-point function of the stress tensor of matter fields in the bulk, we calculate a shear viscosity and find that the ratio with respect to the entanglement entropy density is exactly 1/4π in four dimensions.