Abstract
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.
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Di Dato, A., Gath, J. & Pedersen, A.V. Probing the hydrodynamic limit of (super)gravity. J. High Energ. Phys. 2015, 171 (2015). https://doi.org/10.1007/JHEP04(2015)171
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DOI: https://doi.org/10.1007/JHEP04(2015)171