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The holographic fluid dual to vacuum Einstein gravity

  • Geoffrey Compère
  • Paul McFadden
  • Kostas Skenderis
  • Marika Taylor
Open Access
Article

Abstract

We present an algorithm for systematically reconstructing a solution of the (d + 2)-dimensional vacuum Einstein equations from a (d + 1)-dimensional fluid, extending the non-relativistic hydrodynamic expansion of Bredberg et al. in arXiv:1101.2451 to arbitrary order. The fluid satisfies equations of motion which are the incompressible Navier-Stokes equations, corrected by specific higher-derivative terms. The uniqueness and regularity of this solution is established to all orders and explicit results are given for the bulk metric and the stress tensor of the dual fluid through fifth order in the hydrodynamic expansion. We establish the validity of a relativistic hydrodynamic description for the dual fluid, which has the unusual property of having a vanishing equilibrium energy density. The gravitational results are used to identify transport coefficients of the dual fluid, which also obeys an interesting and exact constraint on its stress tensor. We propose novel Lagrangian models which realise key properties of the holographic fluid.

Keywords

Gauge-gravity correspondence Classical Theories of Gravity 

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Copyright information

© The Author(s) 2011

Open Access This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

Authors and Affiliations

  • Geoffrey Compère
    • 1
  • Paul McFadden
    • 2
  • Kostas Skenderis
    • 1
    • 2
    • 3
  • Marika Taylor
    • 2
    • 3
  1. 1.KdV Institute for MathematicsAmsterdamthe Netherlands
  2. 2.Institute for Theoretical PhysicsAmsterdamthe Netherlands
  3. 3.Gravitation and Astro-Particle Physics AmsterdamAmsterdamthe Netherlands

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