From Navier-Stokes to Einstein
By Irene Bredberg, Cynthia Keeler, V. Lysov, Andrew Strominger. 2011
204 citations recorded by the source corpus.
A bstractWe 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.
Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/fdf6222607ddbca624b54803d5d97f71870695ee
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Citations in the corpus
- Introduction to holographic superconductor models (2015, background): “Another emerging subject is the fluid/gravity correspondence, which translates problems in fluid dynamics into problems in general relativity [236, 237, 238].”
- DE SITTER MUSINGS (2012, methodology): “The problem mimics similar analyses in the context of the near horizon regions of black hole geometries [45, 46, 47, 48, 49, 50] beginning with the seminal work of Damour [51].”
- BMS/GCA redux: towards flatspace holography from non-relativistic symmetries (2012, unknown): “1.1 Flat Space Holography 1 1.2 Galilean Conformal Algebra 2 1.3 An aside: Non-relativistic Hydrodynamics 3 1.4 Outline of the paper 3”