Scalar clouds and the superradiant instability regime of Kerr-Newman black hole

In this paper, we study a physical system that is composed of a massive charged scalar field linearly coupled to a charged rotating Kerr-Newman black hole. Given the parameters of the 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.

Figure 1

The parameter space [half of the ($\mu$, $q$) plane] of the scalar field in the background of Kerr-Newman space-time, which is partitioned by three constraint lines $a$, $b$, and $c$ and the existence line for scalar clouds $\omega ={\omega }_c$. Here, the other parameters are fixed as $n=0$, $l=m=5$, $Q=0.25M$, and $a=0.968235M$.

Figure 2

Left panel: Existence lines (the dot-dashed lines) for nodeless ($n=0$) scalar clouds with various quantum numbers in the ($\mu$, $q$)-parameter space of the scalar field. The dashed line denotes straight line (25), and the solid lines denote hyperbolic curves (23). Right panel: The corresponding ratio between critical frequency ${\omega }_c$ and mass $\mu$ of the scalar cloud as a function of $\mu$. Here, the charge $Q$ and angular momentum $a$ of the black hole are fixed to be $0.25M$ and $0.968235M$, respectively.

Figure 3

Existence lines (the dot-dashed lines) for scalar clouds with given quantum numbers ($n=0$, $l=m=1$) in the ($\mu$, $q$)-parameter space of the scalar field for different black-hole parameters. The dashed lines and the solid lines denote straight line (25) and hyperbolic curves (23), respectively. (Left panel: $Q=0.25M$; right panel: $Q=0.8M$.)