Scalar clouds and the superradiant instability regime of Kerr-Newman   black hole
  In this paper, we study a physical system that is composed of massive charged scalar field linearly coupled to a charged rotating Kerr-Newman black hole. Given the parameters of black hole and a specific set of "quantum" numbers, the parameter space of the scalar field, which is a plane spanned by its mass and charge, is divided into five partitions by three simple constraint lines and the existence line of scalar clouds. The physical properties of the system in these partitions are presented. It is found that superradiant instability may be possibly caused only in two of the partitions. In particular, it is shown that both the mass and charge of the scalar clouds are bounded in a limited region. Our results may be used to rapidly judge the possible occurrence of superradiant instability and the existence of scalar clouds around a given black hole. 
Yang Huang and Dao-Jun Liu
gr-qc