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Phys. J. C"],"published-print":{"date-parts":[[2020,5]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The asymptotically flat, spherical, electro-vacuum black holes (BHs) are shown to support static, spherical configurations of a gauged, self-interacting, scalar field, minimally coupled to the geometry. Considering a <jats:italic>Q<\/jats:italic>-ball type potential for the scalar field, we dub these configurations <jats:italic>Q<\/jats:italic>-<jats:italic>clouds<\/jats:italic>, in the test field approximation. The clouds exist under a <jats:italic>resonance condition<\/jats:italic>, at the threshold of (charged) superradiance. This is similar to the stationary clouds supported by Kerr BHs, which exist for a <jats:italic>synchronisation condition<\/jats:italic>, at the threshold of (rotational) superradiance. In contrast with the rotating case, however, <jats:italic>Q<\/jats:italic>-clouds require the scalar field to be massive <jats:italic>and<\/jats:italic> self-interacting; no similar clouds exist for massive but free scalar fields. First, considering a decoupling limit, we construct <jats:italic>Q<\/jats:italic>-clouds around Schwarzschild and Reissner\u2013Nordstr\u00f6m BHs, showing there is always a mass gap. Then, we make the <jats:italic>Q<\/jats:italic>-clouds backreact, and construct fully non-linear solutions of the Einstein\u2013Maxwell-gauged scalar system describing spherical, charged BHs with resonant, scalar <jats:italic>Q<\/jats:italic>-<jats:italic>hair<\/jats:italic>. Amongst other properties, we observe there is non-uniqueness of charged BHs in this model and the <jats:italic>Q<\/jats:italic>-hairy BHs can be entropically preferred over Reissner\u2013Nordstr\u00f6m, for the same charge to mass ratio; some <jats:italic>Q<\/jats:italic>-hairy BH solutions can be overcharged. We also discuss how some well known no-hair theorems in the literature, applying to electro-vacuum plus minimally coupled scalar fields, are circumvented by this new type of BHs.<\/jats:p>","DOI":"10.1140\/epjc\/s10052-020-7976-9","type":"journal-article","created":{"date-parts":[[2020,5,10]],"date-time":"2020-05-10T09:02:18Z","timestamp":1589101338000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":51,"title":["Spherical electro-vacuum black holes with resonant, scalar Q-hair"],"prefix":"10.1140","volume":"80","author":[{"given":"Carlos A. 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