Black holes as incompressible fluids on the sphere

Abstract

We consider finite deformations of the p + 2-dimensional Schwarzschild geometry which obey the vacuum Einstein equation, preserve the mean curvature and induced conformal metric on a sphere a distance λ from the horizon and are regular on the future horizon. We show perturbatively that in the limit λ → 0 the deformations are given by solutions of the nonlinear incompressible Navier-Stokes equation on the p-sphere. This relation provides a link between global existence for p-dimensional incompressible Navier-Stokes fluids and a novel form of cosmic censorship in p + 2-dimensional general relativity.