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The relativistic fluid dual to vacuum Einstein gravity

The relativistic fluid dual to vacuum Einstein gravity
The relativistic fluid dual to vacuum Einstein gravity
We present a construction of a (d + 2)-dimensional Ricci-flat metric corresponding to a (d + 1)-dimensional relativistic fluid, representing holographically the hydrodynamic regime of a (putative) dual theory. We show how to obtain the metric to arbitrarily high order using a relativistic gradient expansion, and explicitly carry out the computation to second order. The fluid has zero energy density in equilibrium, which implies incompressibility at first order in gradients, and its stress tensor (both at and away from equilibrium) satisfies a quadratic constraint, which determines its energy density away from equilibrium. The entire dynamics to second order is encoded in one first order and six second order transport coefficients, which we compute. We classify entropy currents with non-negative divergence at second order in relativistic gradients. We then verify that the entropy current obtained by pulling back to the fluid surface the area form at the null horizon indeed has a non-negative divergence. We show that there are distinct near-horizon scaling limits that are equivalent either to the relativistic gradient expansion we discuss here, or to the non-relativistic expansion associated with the Navier-Stokes equations discussed in previous works. The latter expansion may be recovered from the present relativistic expansion upon taking a specific non-relativistic limit.
gauge-gravity correspondence, classical theories of gravity
1-29
Compere, Geoffrey
0617f69a-a53c-49ef-afba-b0ca17657aa7
McFadden, Paul
4e7762ff-9b96-4516-b333-be01784fdbae
Skenderis, Konstantinos
09f32871-ffb1-4f4a-83bc-df05f4d17a09
Taylor, Marika
5515acab-1bed-4607-855a-9e04252aec22
Compere, Geoffrey
0617f69a-a53c-49ef-afba-b0ca17657aa7
McFadden, Paul
4e7762ff-9b96-4516-b333-be01784fdbae
Skenderis, Konstantinos
09f32871-ffb1-4f4a-83bc-df05f4d17a09
Taylor, Marika
5515acab-1bed-4607-855a-9e04252aec22

Compere, Geoffrey, McFadden, Paul, Skenderis, Konstantinos and Taylor, Marika (2012) The relativistic fluid dual to vacuum Einstein gravity. Journal of High Energy Physics, 2012 (76), 1-29. (doi:10.1007/JHEP03(2012)076).

Record type: Article

Abstract

We present a construction of a (d + 2)-dimensional Ricci-flat metric corresponding to a (d + 1)-dimensional relativistic fluid, representing holographically the hydrodynamic regime of a (putative) dual theory. We show how to obtain the metric to arbitrarily high order using a relativistic gradient expansion, and explicitly carry out the computation to second order. The fluid has zero energy density in equilibrium, which implies incompressibility at first order in gradients, and its stress tensor (both at and away from equilibrium) satisfies a quadratic constraint, which determines its energy density away from equilibrium. The entire dynamics to second order is encoded in one first order and six second order transport coefficients, which we compute. We classify entropy currents with non-negative divergence at second order in relativistic gradients. We then verify that the entropy current obtained by pulling back to the fluid surface the area form at the null horizon indeed has a non-negative divergence. We show that there are distinct near-horizon scaling limits that are equivalent either to the relativistic gradient expansion we discuss here, or to the non-relativistic expansion associated with the Navier-Stokes equations discussed in previous works. The latter expansion may be recovered from the present relativistic expansion upon taking a specific non-relativistic limit.

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Accepted/In Press date: 5 March 2012
Published date: 23 March 2012
Keywords: gauge-gravity correspondence, classical theories of gravity
Organisations: Applied Mathematics

Identifiers

Local EPrints ID: 385149
URI: http://eprints.soton.ac.uk/id/eprint/385149
PURE UUID: e2db6abb-620f-4965-8d29-e23ba0da1f1d
ORCID for Konstantinos Skenderis: ORCID iD orcid.org/0000-0003-4509-5472
ORCID for Marika Taylor: ORCID iD orcid.org/0000-0001-9956-601X

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Date deposited: 15 Jan 2016 16:41
Last modified: 21 Nov 2021 03:06

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Contributors

Author: Geoffrey Compere
Author: Paul McFadden
Author: Marika Taylor ORCID iD

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