Electrically charged black holes with electroweak hair

Abstract

We construct electrically charged black holes in Einstein's gravity coupled to the bosonic sector of the electroweak theory, focusing on static, spherically symmetric and asymptotically flat solutions, with the weak mixing angle fixed to its Standard Model value. Horizon regularity imposes a resonance condition relating the charged-vector frequency to the electromagnetic potential at the horizon, corresponding to the threshold of charged superradiance. A perturbative analysis further shows that nonextremal Reissner-Nordström black holes do not support regular, exponentially localized, spherically symmetric electroweak clouds satisfying such condition. Thus, the hairy solutions cannot emerge via a bifurcation from this electrovacuum family. Moreover, our numerical investigation reveals two apparently disconnected families of bosonic stars. Within the explored parameter space, the hairy black holes are connected to the strongly gravitating one.