Probing the Hydrodynamic Limit of (Super)gravity

TL;DR

This paper investigates the hydrodynamic behavior of charged black branes in supergravity, deriving their transport properties, analyzing stability, and confirming theoretical predictions through cross-checks.

Contribution

It provides a detailed effective hydrodynamic description of charged dilatonic black branes, including stability analysis and transport coefficient calculations, extending previous mappings.

Findings

Stable charged configurations exist in certain parameter regimes.

Maxwell charged branes are generally Gregory-Laflamme unstable.

Cross-checks confirm the consistency of transport coefficients with prior results.

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.