Arias, RaúlMas Solé, JavierSerantes Rubianes, Alexandre2017-10-192017-10-192016-09-06Arias, R., Mas, J. & Serantes, A. J. High Energ. Phys. (2016) 2016: 24. https://doi.org/10.1007/JHEP09(2016)024http://hdl.handle.net/10347/15879We study linear and nonlinear stability of asymptotically AdS4 solutions in Einstein-Maxwell-scalar theory. After summarizing the set of static solutions we first examine thermodynamical stability in the grand canonical ensemble and the phase transitions that occur among them. In the second part of the paper we focus on nonlinear stability in the microcanonical ensemble by evolving radial perturbations numerically. We find hints of an instability corner for vanishingly small perturbations of the same kind as the ones present in the uncharged case. Collapses are avoided, instead, if the charge and mass of the perturbations come to close the line of solitons. Finally we examine the soliton solutions. The linear spectrum of normal modes is not resonant and instability turns on at extrema of the mass curve. Linear stability extends to nonlinear stability up to some threshold for the amplitude of the perturbation. Beyond that, the soliton is destroyed and collapses to a hairy black hole. The relative width of this stability band scales down with the charge Q, and does not survive the blow up limit to a planar geometry.eng© The Author(s) 2016. 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 creditedhttps://creativecommons.org/licenses/by/4.0/AdS-CFT CorrespondenceBlack HolesClassical Theories of GravityHolography and condensed matter physics (AdS/CMT)Materias::Investigación::22 Física::2212 Física teóricajournal article10.1007/JHEP09(2016)0241029-8479open access