Spherically Symmetric Scalar Hair for Charged Black Holes

The no-hair theorem by Mayo and Bekenstein states that there exists no non-extremal 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, 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 paper, 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-Nordstr\"{o}m black hole, is a good approximation to Q-hair under a certain limit.