Black Holes as Incompressible Fluids on the Sphere
High Energy Physics - Theory
2015-05-28 v1 General Relativity and Quantum Cosmology
Fluid Dynamics
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 from the horizon and are regular on the future horizon. We show perturbatively that in the limit 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.
Cite
@article{arxiv.1106.3084,
title = {Black Holes as Incompressible Fluids on the Sphere},
author = {Irene Bredberg and Andrew Strominger},
journal= {arXiv preprint arXiv:1106.3084},
year = {2015}
}