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Black holes as incompressible fluids on the sphere

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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.

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Authors and Affiliations

  1. Center for the Fundamental Laws of Nature, Harvard University, Cambridge, MA, 02138, USA

    Irene Bredberg & Andrew Strominger

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  1. Irene Bredberg
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  2. Andrew Strominger
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Correspondence to Irene Bredberg.

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ArXiv ePrint: 1106.3084

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Bredberg, I., Strominger, A. Black holes as incompressible fluids on the sphere. J. High Energ. Phys. 2012, 43 (2012). https://doi.org/10.1007/JHEP05(2012)043

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  • DOI: https://doi.org/10.1007/JHEP05(2012)043

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