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 $\lambda$ from the horizon and are regular on the future horizon. We show perturbatively that in the limit $\lambda$ approaches 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.

References in corpus (4)

• Nonlinear Fluid Dynamics from Gravity
• The Incompressible Non-Relativistic Navier-Stokes Equation from Gravity
• The holographic fluid dual to vacuum Einstein gravity
• The Penrose Inequality and the Fluid/Gravity Correspondence

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