Local Fluid Dynamical Entropy from Gravity

Bhattacharyya, Sayantani; Hubeny, Veronika E.; Loganayagam, R.; Mandal, Gautam; Minwalla, Shiraz; Rangamani, Mukund; Reall, Harvey S.

doi:10.1088/1126-6708/2008/06/055

Local Fluid Dynamical Entropy from Gravity

Bhattacharyya, Sayantani; Hubeny, Veronika E.; Loganayagam, R.; Mandal, Gautam; Minwalla, Shiraz; Rangamani, Mukund; Reall, Harvey S.

Authors

Sayantani Bhattacharyya

Veronika E. Hubeny

R. Loganayagam

Gautam Mandal

Shiraz Minwalla

Mukund Rangamani

Harvey S. Reall

Abstract

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.

Citation

Bhattacharyya, S., Hubeny, V. E., Loganayagam, R., Mandal, G., Minwalla, S., Rangamani, M., & Reall, H. S. (2008). Local Fluid Dynamical Entropy from Gravity. Journal of High Energy Physics, 2008(06), Article 055. https://doi.org/10.1088/1126-6708/2008/06/055

Journal Article Type	Article
Publication Date	Jun 13, 2008
Deposit Date	Nov 24, 2010
Publicly Available Date	Sep 11, 2012
Journal	Journal of High Energy Physics
Print ISSN	1126-6708
Electronic ISSN	1029-8479
Publisher	Scuola Internazionale Superiore di Studi Avanzati (SISSA)
Peer Reviewed	Peer Reviewed
Volume	2008
Issue	06
Article Number	055
DOI	https://doi.org/10.1088/1126-6708/2008/06/055
Keywords	AdS-CFT and dS-CFT Correspondence, Black Holes in String Theory, Gauge-gravity correspondence.