D = 5 static, charged black holes, strings and rings with resonant, scalar Q-hair

Abstract

A mechanism for circumventing the Mayo-Bekenstein no-hair theorem allows endowing four dimensional (D = 4) asymptotically flat, spherical, electro-vacuum black holes with a minimally coupled U(1)-gauged scalar field profile: Q-hair. The scalar field must be massive, self-interacting and obey a resonance condition at the threshold of (charged) superradiance. We establish generality for this mechanism by endowing three different types of static black objects with scalar hair, within a D = 5 Einstein-Maxwellgauged scalar field model: asymptotically flat black holes and black rings; and black strings which asymptote to a Kaluza-Klein vacuum. These D = 5 Q-hairy black objects share many of the features of their D = 4 counterparts. In particular, the scalar field is subject to a resonance condition and possesses a Q-ball type potential. For the static black ring, the charged scalar hair can balance it, yielding solutions that are singularity free on and outside the horizon.