Bhattacharyya, Sayantani ; Loganayagam, R. ; Minwalla, Shiraz ; Nampuri, Suresh ; Trivedi, Sandip P. ; Wadia, Spenta R. (2009) Forced fluid dynamics from gravity Journal of High Energy Physics, 2009 (2). 018_1-018_50. ISSN 1126-6708
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Official URL: http://iopscience.iop.org/1126-6708/2009/02/018?fr...
Related URL: http://dx.doi.org/10.1088/1126-6708/2009/02/018
Abstract
We generalize the computations of [1] to generate long wavelength, asymptotically locally AdS5 solutions to the Einstein-dilaton system with a slowly varying boundary dilaton field and a weakly curved boundary metric. Upon demanding regularity , our solutions are dual, under the AdS/CFT correspondence, to arbitrary fluid flows in the boundary theory formulated on a weakly curved manifold with a prescribed slowly varying coupling constant. These solutions turn out to be parameterized by four-velocity and temperature fields that are constrained to obey the boundary covariant Navier Stokes equations with a dilaton dependent forcing term. We explicitly evaluate the stress tensor and Lagrangian as a function of the velocity, temperature, coupling constant and curvature fields, to second order in the derivative expansion and demonstrate the Weyl covariance of these expressions. We also construct the event horizon of the dual solutions to second order in the derivative expansion, and use the area form on this event horizon to construct an entropy current for the dual fluid. As a check of our constructions we expand the exactly known solutions for rotating black holes in global AdS5 in a boundary derivative expansion and find perfect agreement with all our results upto second order. We also find other simple solutions of the forced fluid mechanics equations and discuss their bulk interpretation. Our results may aid in determining a bulk dual to forced flows exhibiting steady state turbulence.
Item Type: | Article |
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Source: | Copyright of this article belongs to Institute of Physics. |
Keywords: | Black Holes; AdS-CFT and dS-CFT Correspondence; Black Holes in String Theory |
ID Code: | 57608 |
Deposited On: | 27 Aug 2011 15:05 |
Last Modified: | 18 May 2016 08:57 |
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