https://doi.org/10.1140/epjc/s10052-020-7976-9
Regular Article - Theoretical Physics
Spherical electro-vacuum black holes with resonant, scalar Q-hair
Departamento de Matemática da Universidade de Aveiro and Centre for Research and Development in Mathematics and Applications (CIDMA), Campus de Santiago, 3810-183, Aveiro, Portugal
* e-mail: eugen.radu@ua.pt
Received:
6
April
2020
Accepted:
26
April
2020
Published online:
10
May
2020
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.
© The Author(s), 2020
