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Towards a general fluid/gravity correspondence

Towards a general fluid/gravity correspondence
Towards a general fluid/gravity correspondence
We set up the construction of generic (d+2)-dimensional metrics corresponding to (d+1)-dimensional fluids, representing holographically the hydrodynamic regimes of the putative dual theories. We give general seed equilibrium metrics appropriate to generic bulk stress energy tensors and discuss the implications of conformal rescalings of the hypersurface on which the fluid is defined. We then show how to obtain the corresponding hydrodynamic metrics using a relativistic gradient expansion and discuss the integrability conditions of the resulting equations. The stress energy tensors of the resulting fluids, both at and away from equilibrium, satisfy a quadratic constraint. We interpret this constraint in terms of two possible equations of state for the fluid and show that only one of the two equations is physical. We illustrate our discussions with the example of the cutoff anti–de Sitter fluid, for which we find the precise interpretation in terms of deformations of the UV conformal field theory. Finally we discuss the relation between the modern fluid/gravity approach taken in this paper and the earlier membrane paradigm.
1550-7998
1-33
Pinzani-Fokeeva, Natalia
d3137cda-54e5-49d5-ab54-c3c54d387d0e
Taylor, Marika
5515acab-1bed-4607-855a-9e04252aec22
Pinzani-Fokeeva, Natalia
d3137cda-54e5-49d5-ab54-c3c54d387d0e
Taylor, Marika
5515acab-1bed-4607-855a-9e04252aec22

Pinzani-Fokeeva, Natalia and Taylor, Marika (2015) Towards a general fluid/gravity correspondence. Physical Review D, 91 (4), 1-33. (doi:10.1103/PhysRevD.91.044001).

Record type: Article

Abstract

We set up the construction of generic (d+2)-dimensional metrics corresponding to (d+1)-dimensional fluids, representing holographically the hydrodynamic regimes of the putative dual theories. We give general seed equilibrium metrics appropriate to generic bulk stress energy tensors and discuss the implications of conformal rescalings of the hypersurface on which the fluid is defined. We then show how to obtain the corresponding hydrodynamic metrics using a relativistic gradient expansion and discuss the integrability conditions of the resulting equations. The stress energy tensors of the resulting fluids, both at and away from equilibrium, satisfy a quadratic constraint. We interpret this constraint in terms of two possible equations of state for the fluid and show that only one of the two equations is physical. We illustrate our discussions with the example of the cutoff anti–de Sitter fluid, for which we find the precise interpretation in terms of deformations of the UV conformal field theory. Finally we discuss the relation between the modern fluid/gravity approach taken in this paper and the earlier membrane paradigm.

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More information

e-pub ahead of print date: 2 February 2015
Published date: 15 February 2015
Organisations: Applied Mathematics

Identifiers

Local EPrints ID: 385156
URI: http://eprints.soton.ac.uk/id/eprint/385156
ISSN: 1550-7998
PURE UUID: c89acbd1-c185-4b1b-b13c-6c0689529364
ORCID for Marika Taylor: ORCID iD orcid.org/0000-0001-9956-601X

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Date deposited: 18 Jan 2016 09:22
Last modified: 21 Nov 2021 03:06

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Contributors

Author: Natalia Pinzani-Fokeeva
Author: Marika Taylor ORCID iD

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