From Navier-Stokes to Einstein View Full Text


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Article Info

DATE

2012-07

AUTHORS

Irene Bredberg, Cynthia Keeler, Vyacheslav Lysov, Andrew Strominger

ABSTRACT

We show by explicit construction that for every solution of the incompressible Navier-Stokes equation in p + 1 dimensions, there is a uniquely associated “dual” solution of the vacuum Einstein equations in p + 2 dimensions. The dual geometry has an intrinsically flat timelike boundary segment Σc whose extrinsic curvature is given by the stress tensor of the Navier-Stokes fluid. We consider a “near-horizon” limit in which Σc becomes highly accelerated. The near-horizon expansion in gravity is shown to be mathematically equivalent to the hydrodynamic expansion in fluid dynamics, and the Einstein equation reduces to the incompressible Navier-Stokes equation. For p = 2, we show that the full dual geometry is algebraically special Petrov type II. The construction is a mathematically precise realization of suggestions of a holographic duality relating fluids and horizons which began with the membrane paradigm in the 70’s and resurfaced recently in studies of the AdS/CFT correspondence. More... »

PAGES

146

Journal

TITLE

Journal of High Energy Physics

ISSUE

7

VOLUME

2012

Author Affiliations

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/jhep07(2012)146

DOI

http://dx.doi.org/10.1007/jhep07(2012)146

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1030510499


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