From Navier-Stokes to Einstein

Irene Bredberg, Cynthia Keeler, Vyacheslav Lysov, Andrew Strominger

Research output: Contribution to journalArticle

71 Citations (Scopus)

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 Σ c whose extrinsic curvature is given by the stress tensor of the Navier-Stokes fluid. We consider a "near-horizon" limit in which Σ c 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.

Original languageEnglish (US)
Article number146
JournalJournal of High Energy Physics
Volume2012
Issue number7
DOIs
StatePublished - Aug 6 2012
Externally publishedYes

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horizon
Einstein equations
Navier-Stokes equation
expansion
fluids
stress tensors
fluid dynamics
geometry
suggestion
hydrodynamics
curvature
gravitation
membranes
vacuum

Keywords

  • Black holes
  • Classical theories of gravity
  • Holography and condensed matter physics (AdS/CMT)

ASJC Scopus subject areas

  • Nuclear and High Energy Physics

Cite this

From Navier-Stokes to Einstein. / Bredberg, Irene; Keeler, Cynthia; Lysov, Vyacheslav; Strominger, Andrew.

In: Journal of High Energy Physics, Vol. 2012, No. 7, 146, 06.08.2012.

Research output: Contribution to journalArticle

Bredberg, Irene ; Keeler, Cynthia ; Lysov, Vyacheslav ; Strominger, Andrew. / From Navier-Stokes to Einstein. In: Journal of High Energy Physics. 2012 ; Vol. 2012, No. 7.
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