Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2011-01-12
Physics
High Energy Physics
High Energy Physics - Theory
15 pages, 2 figures, typos corrected
Scientific paper
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 $\Sigma_c$ whose extrinsic curvature is given by the stress tensor of the Navier-Stokes fluid. We consider a "near-horizon" limit in which $\Sigma_c$ 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.
Bredberg Irene
Keeler Cynthia
Lysov Vyacheslav
Strominger Andrew
No associations
LandOfFree
From Navier-Stokes To Einstein does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with From Navier-Stokes To Einstein, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and From Navier-Stokes To Einstein will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-65526