Exact Regions of Superradiant Instability of Kerr-Newman Black Holes and Massive Scalar Fields

TL;DR

This paper analytically characterizes the exact parameter regions where Kerr-Newman black holes exhibit superradiant instability due to massive charged scalar fields, providing precise boundaries and growth rates without numerical approximation.

Contribution

It derives exact analytic expressions for instability boundaries and growth rates, clarifying the parameter space of superradiant instability in Kerr-Newman black holes.

Findings

Instability region shifts from neutral to highly charged black holes as scalar mass increases.

Exact analytic expressions for instability boundaries and growth rates are obtained.

Superradiant instability is absent in the Reissner-Nordstrom limit.

Abstract

We investigate the superradiant instability of Kerr-Newman black holes in the presence of a massive, charged scalar field using the Vieira-Bezerra-Kokkotas (VBK) method. We study the solutions of the exact polynomial condition for quasibound state frequencies and determine the domain of superradiant instability in parameter space without relying on the hydrogenic approximation or numerics. We derive the minimum scalar mass needed for quasibound states to exist, and identify the precise overlap region between the quasibound and superradiant conditions where instability can occur. We obtain perturbative and exact analytic expressions for the instability boundaries and growth rates, and clarify their relation to previous numerical results. Our analysis reveals how the instability region shifts from nearly neutral Kerr black holes for light fields to highly charged near-extremal Kerr-Newman black holes for heavier fields, while remaining absent in the Reissner-Nordstrom limit.