Probing the hydrodynamic limit of (super)gravity
- 247 Downloads
We study the long-wavelength effective description of two general classes of charged dilatonic (asymptotically flat) black p-branes including D/NS/M-branes in ten and eleven dimensional supergravity. In particular, we consider gravitational brane solutions in a hydrodynamic derivative expansion (to first order) for arbitrary dilaton coupling and for general brane and co-dimension and determine their effective electro-fluid-dynamic descriptions by exacting the characterizing transport coefficients. We also investigate the stability properties of the corresponding hydrodynamic systems by analyzing their response to small long-wavelength perturbations. For branes carrying unsmeared charge, we find that in a certain regime of parameter space there exists a branch of stable charged configurations. This is in accordance with the expectation that D/NS/M-branes have stable configurations, except for the D5, D6, and NS5. In contrast, we find that Maxwell charged brane configurations are Gregory-Laflamme unstable independently of the charge and, in particular, verify that smeared configurations of D0-branes are unstable. Finally, we provide a modification to the mapping presented in arXiv:1211.2815 and utilize it to provide a non-trivial cross-check on a certain subset of our transport coefficients with the results of arXiv:1110.2320.
Keywordsp-branes Black Holes in String Theory D-branes AdS-CFT Correspondence
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
- L.D. Landau and E.M. Lifshitz, Fluid mechanics, 2nd edition, Course of theoretical physics volume 6. Pergamon Press, London (1987).Google Scholar
- J. Gath and A.V. Pedersen, work in progress.Google Scholar