Nonlinear Fluid Dynamics from Gravity

Bhattacharyya, Sayantani; Minwalla, Shiraz; Hubeny, Veronika E; Rangamani, Mukund

Abstract

Black branes in AdS5 appear in a four parameter family labeled by their velocity and temperature. Promoting these parameters to Goldstone modes or collective coordinate fields—arbitrary functions of the coordinates on the boundary of AdS5—we use Einstein's equations together with regularity requirements and boundary conditions to determine their dynamics. The resultant equations turn out to be those of boundary fluid dynamics, with specific values for fluid parameters. Our analysis is perturbative in the boundary derivative expansion but is valid for arbitrary amplitudes. Our work may be regarded as a derivation of the nonlinear equations of boundary fluid dynamics from gravity. As a concrete application we find an explicit expression for the expansion of this fluid stress tensor including terms up to second order in the derivative expansion.

Citation

Bhattacharyya, S., Minwalla, S., Hubeny, V. E., & Rangamani, M. (2008). Nonlinear Fluid Dynamics from Gravity. Journal of High Energy Physics, 2008(02), Article 045. https://doi.org/10.1088/1126-6708/2008/02/045

• Journal Article Type: Article
• Publication Date: Feb 14, 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: 02
• Article Number: 045
• DOI: https://doi.org/10.1088/1126-6708/2008/02/045
• Keywords: AdS-CFT and dS-CFT Correspondence, Gauge-gravity correspondence.
• Public URL: https://durham-repository.worktribe.com/output/1513016
• Publisher URL: http://iopscience.iop.org/1126-6708/2008/02/045/