Spherically Symmetric Scalar Hair for Charged Black Holes

The no-hair theorem by Mayo and Bekenstein states that there exists no nonextremal static and spherical charged black hole endowed with hair in the form of a charged scalar field with a self-interaction potential. In our recent work [Phys. Lett. B 803, 135324 (2020)], we showed that the effect of a scalar mass term is important at an asymptotic infinity, which was omitted to prove the no-hair theorem. In this Letter, we demonstrate that there actually exists static and spherical charged scalar hair, dubbed as Q hair, around charged black holes, by taking into account the backreaction to the metric and gauge field. We also discuss that Q cloud, which is constructed without the backreaction around a Reissner-Nordström black hole, is a good approximation to Q hair under a certain limit.