On the instability for massive scalar fields in Kerr-Newman spacetime

TL;DR

This paper numerically investigates the superradiant instability of massive charged scalar fields around Kerr-Newman black holes, revealing finite unstable regions, enhanced growth rates due to electromagnetic interactions, and specific bounds on scalar cloud masses.

Contribution

It provides a detailed numerical analysis of superradiant instability in Kerr-Newman spacetime, highlighting the effects of charge and rotation on instability growth rates and mode bounds.

Findings

Unstable scalar modes occur only in finite parameter regions.

Electromagnetic interaction increases the instability growth rate by 15.7%.

Maximum growth rate found is 4% higher than in Kerr spacetime.

Abstract

It is known that a massive charged scalar field can trigger a superradiant instability in the background of a Kerr-Newman black hole. In this paper, we present a numerical study of such an instability by using the continued fraction method. It is shown that for given a black hole, the unstable scalar mode with a specific azimuthal index $m$ only occurs in a finite region in the parameter space of the scalar field. The maximum mass of the scalar cloud is exactly the upper bound of the mass of the unstable modes. We show that due to the electromagnetic interaction between the scalar field and the Kerr-Newman black hole, the growth rate of the instability can be $15.7\%$ larger than that of a scalar field in Kerr spacetime of the same rotation parameter. In addition, we find a maximum value of the growth rate $\tau^{-1}=1.788\times 10^{-7}M^{-1}$, which is about $4\%$ larger than that in the Kerr case.