BSM

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. We consider both a "near-horizon" limit in which $\Sigma_c$ becomes highly accelerated, and a long-wavelength hydrodynamic limit. We show that the near-horizon expansion in gravity is mathematically equivalent to the hydrodynamic expansion in fluid dynamics, and the Einstein equation reduces to the incompressible Navier-Stokes equation.