Spherical electro-vacuum black holes with resonant, scalar $Q$-hair

Abstract

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 $Q$-ball type potential for the scalar field, we dub these configurations $Q$-clouds, in the test field approximation. The clouds exist under a resonance condition, at the threshold of (charged) superradiance. This is similar to the stationary clouds supported by Kerr BHs, which exist for a synchronisation condition, at the threshold of (rotational) superradiance. In contrast with the rotating case, however, $Q$-clouds require the scalar field to be massive and self-interacting; no similar clouds exist for massive but free scalar fields. First, considering a decoupling limit, we construct $Q$-clouds around Schwarzschild and Reissner-Nordström BHs, showing there is always a mass gap. Then, we make the $Q$-clouds backreact, and construct fully non-linear solutions of the Einstein-Maxwell-gauged scalar system describing spherical, charged BHs with resonant, scalar $Q$-hair. Amongst other properties, we observe there is non-uniqueness of charged BHs in this model and the $Q$-hairy BHs can be entropically preferred over Reissner-Nordström, for the same charge to mass ratio; some $Q$-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.

18 pages, 5 figures; v2. typos corrected, matches published version

References in corpus (9)

• Non-linear Q-clouds around Kerr black holes
• Myers-Perry black holes with scalar hair and a mass gap
• Kerr-Newman black holes with scalar hair
• Myers-Perry black holes with scalar hair and a mass gap: unequal spins
• Charged Proca Stars
• Marginal scalar and Proca clouds around Reissner-Nordström black holes
• Charged Q-balls and boson stars and dynamics of charged test particles
• Boson Shells Harbouring Charged Black Holes
• Violations of the Kerr and Reissner-Nordstrom bounds: horizon versus asymptotic quantities

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