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. © 2012 American Institute of Physics.
Hydrodynamics and viscosity in the Rindler spacetime / Eling, C.; Chirco, G.; Liberati, S.. - 1458:(2011), pp. 69-83. (Intervento presentato al convegno Spanish Relativity Meeting 2011: Towards New Paradigms, ERE2011 tenutosi a Madrid, esp nel 2011) [10.1063/1.4734405].
Hydrodynamics and viscosity in the Rindler spacetime
Chirco G.;
2011
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. © 2012 American Institute of Physics.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.