AdS/Ricci-flat correspondence and the Gregory-Laflamme instability
AdS/Ricci-flat correspondence and the Gregory-Laflamme instability
We show that for every asymptotically anti–de Sitter (AdS) solution compactified on a torus there is a corresponding Ricci-flat solution obtained by replacing the torus by a sphere, performing a Weyl rescaling of the metric and appropriately analytically continuing the dimension of the torus/sphere (as in generalized dimensional reduction). In particular, it maps Minkowski spacetime to AdS on a torus, the holographic stress energy tensor of AdS to the stress energy tensor due to a brane localized in the interior of spacetime and AdS black branes to (asymptotically flat) Schwarzschild black branes. Applying it to the known solutions describing the hydrodynamic regime in AdS/CFT, we derive the hydrodynamic stress tensor of asymptotically flat black branes to second order, which is constrained by the parent conformal symmetry. We compute the dispersion relation of the Gregory-Laflamme unstable modes through cubic order in the wave number, finding remarkable agreement with numerical data. In the case of no transverse sphere, AdS black branes are mapped to Rindler spacetime and the second-order transport coefficients of the fluid dual to Rindler spacetime are recovered.
1-6
Caldarelli, Marco M.
873ef6f9-92c0-48f6-8362-6b1bee12d540
Camps, Joan
499e5cd2-cb05-488b-a205-4cdc672ddbf7
Goutéraux, Blaise
17b64af4-5a32-490c-8ed1-75b78c12a308
Skenderis, Kostas
09f32871-ffb1-4f4a-83bc-df05f4d17a09
19 March 2013
Caldarelli, Marco M.
873ef6f9-92c0-48f6-8362-6b1bee12d540
Camps, Joan
499e5cd2-cb05-488b-a205-4cdc672ddbf7
Goutéraux, Blaise
17b64af4-5a32-490c-8ed1-75b78c12a308
Skenderis, Kostas
09f32871-ffb1-4f4a-83bc-df05f4d17a09
Caldarelli, Marco M., Camps, Joan, Goutéraux, Blaise and Skenderis, Kostas
(2013)
AdS/Ricci-flat correspondence and the Gregory-Laflamme instability.
Physical Review D, 87 (61502), .
(doi:10.1103/PhysRevD.87.061502).
Abstract
We show that for every asymptotically anti–de Sitter (AdS) solution compactified on a torus there is a corresponding Ricci-flat solution obtained by replacing the torus by a sphere, performing a Weyl rescaling of the metric and appropriately analytically continuing the dimension of the torus/sphere (as in generalized dimensional reduction). In particular, it maps Minkowski spacetime to AdS on a torus, the holographic stress energy tensor of AdS to the stress energy tensor due to a brane localized in the interior of spacetime and AdS black branes to (asymptotically flat) Schwarzschild black branes. Applying it to the known solutions describing the hydrodynamic regime in AdS/CFT, we derive the hydrodynamic stress tensor of asymptotically flat black branes to second order, which is constrained by the parent conformal symmetry. We compute the dispersion relation of the Gregory-Laflamme unstable modes through cubic order in the wave number, finding remarkable agreement with numerical data. In the case of no transverse sphere, AdS black branes are mapped to Rindler spacetime and the second-order transport coefficients of the fluid dual to Rindler spacetime are recovered.
Text
1211.2815.pdf
- Accepted Manuscript
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Published date: 19 March 2013
Organisations:
Applied Mathematics
Identifiers
Local EPrints ID: 391645
URI: http://eprints.soton.ac.uk/id/eprint/391645
ISSN: 1550-7998
PURE UUID: 1f938328-de4e-4bab-92de-d6d30afafdfc
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Date deposited: 24 May 2016 14:23
Last modified: 15 Mar 2024 03:41
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Contributors
Author:
Marco M. Caldarelli
Author:
Joan Camps
Author:
Blaise Goutéraux
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