Black Holes as Incompressible Fluids on the Sphere

TL;DR

This paper establishes a perturbative connection between deformations of Schwarzschild black holes and solutions to the incompressible Navier-Stokes equations on a sphere, linking fluid dynamics and gravitational physics.

Contribution

It demonstrates that near the horizon, black hole deformations correspond to incompressible fluid flows on a sphere, revealing a novel link between gravity and fluid dynamics.

Findings

Deformations obeying Einstein's equations relate to Navier-Stokes solutions.

The limit as pproaches 0 yields the nonlinear incompressible Navier-Stokes equation.

Provides a new perspective on cosmic censorship via 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 $\lambda$ 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.