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Local fluid dynamical entropy from gravity.

Bhattacharyya, Sayantani and Hubeny, Veronika E. and Loganayagam, R. and Mandal, Gautam and Minwalla, Shiraz and Rangamani, Mukund and Reall, Harvey S. (2008) 'Local fluid dynamical entropy from gravity.', Journal of high energy physics., 2008 (06). 055.


Spacetime geometries dual to arbitrary fluid flows in strongly coupled = 4 super Yang Mills theory have recently been constructed perturbatively in the long wavelength limit. We demonstrate that these geometries all have regular event horizons, and determine the location of the horizon order by order in a boundary derivative expansion. Intriguingly, the derivative expansion allows us to determine the location of the event horizon in the bulk as a local function of the fluid dynamical variables. We define a natural map from the boundary to the horizon using ingoing null geodesics. The area-form on spatial sections of the horizon can then be pulled back to the boundary to define a local entropy current for the dual field theory in the hydrodynamic limit. The area theorem of general relativity guarantees the positivity of the divergence of the entropy current thus constructed.

Item Type:Article
Keywords:AdS-CFT and dS-CFT Correspondence, Black Holes in String Theory, Gauge-gravity correspondence.
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Publisher statement:© SISSA 2008. Published by IOP Publishing for SISSA. This is an author-created, un-copyedited version of an article accepted for publication in Journal of high energy physics. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at 10.1088/1126-6708/2008/06/055.
Record Created:07 Sep 2012 10:20
Last Modified:17 Jun 2015 12:35

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