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2011

Black Holes as Incompressible Fluids on the Sphere

Bredberg, Irene, Strominger, Andrew

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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.

Black Holes as Incompressible Fluids on the Sphere · Around

Built on

I. Bredberg, C. Keeler, V. Lysov and A. Strominger, “Wilsonian Approach to Fluid/Gravity Duality,” arXiv:1006.1902 [hep-th]
Original
1902
Earlier work this paper cites.
T. Damour, in: “Quelques propriétés mécaniques, électromagnétiques, thermodynamiques et quantiques des trous noirs”; Thèse de Doctorat d’Etat, Université Pierre et Marie Curie, Paris VI, 1979
1979
Earlier work this paper cites.
T. Damour, “Surface effects in Black Hole Physics,” in Proceedings of the second Marcel Grossmann Meeting on general Relativity
1982
Earlier work this paper cites.

Similar

R. H. Price and K. S. Thorne, “Membrane Viewpoint on Black Holes: Properties and eEvolution of the Stretched Horizon,” Phys. Rev. D 33
1986
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G. Policastro, D. T. Son and A. O. Starinets, “The shear viscosity of strongly coupled N = 4 supersymmetric Yang-Mills plasma,” Phys. Rev. Lett. 87
2001
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I. Bredberg, C. Keeler, V. Lysov and A. Strominger, “From Navier-Stokes to Einstein,” arXiv:1101.2451 [hep-th]
Original
Cited in the paper.
G. Compere, P. McFadden, K. Skenderis, M. Taylor, “The Holographic fluid dual to vacuum Einstein gravity,” [arXiv:1103.3022 [hep-th]]
Original
Cited in the paper.
V. Lysov, A. Strominger, “From Petrov-Einstein to Navier-Stokes,” [arXiv:1104.5502 [hep-th]]
Original
Cited in the paper.

Then

S. Bhattacharyya, S. Minwalla and S. R. Wadia, “The Incompressible Non-Relativistic Navier-Stokes Equation from Gravity,” JHEP 0908
Original
2009
Later among the works it cites.
Y. Oz, M. Rabinovich, “The Penrose Inequality and the Fluid/Gravity Correspondence,” JHEP 1102
Original
2011
Closest in time.

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