Local Fluid Dynamical Entropy from Gravity

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

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.
• Public URL: https://durham-repository.worktribe.com/output/1545774