From Navier-Stokes To Einstein
Jan, 2011
Citations per year
Abstract: (arXiv)
We show by explicit construction that for every solution of the incompressible Navier-Stokes equation in dimensions, there is a uniquely associated "dual" solution of the vacuum Einstein equations in dimensions. The dual geometry has an intrinsically flat timelike boundary segment whose extrinsic curvature is given by the stress tensor of the Navier-Stokes fluid. We consider a "near-horizon" limit in which 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 , 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.Note:
- 15 pages, 2 figures, typos corrected
- duality: holography
- Einstein equation: vacuum
- expansion: hydrodynamics
- tensor: energy-momentum
- Navier-Stokes equation
- any-dimensional
- Einstein equation: solution
References(48)
Figures(2)