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

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.

v2: 16 pages plus acknowledgments and references, 5 figures; minor typos corrected, references added, equations streamlined, fig. 1 and 2 combined into 1, 2nd-order result improved, exact result found and added, improvements and additions reflected in fig. 5 with N changed from 0 to 1; v3: typos corrected, added comments to clarify units, published version; v4: corrected eq 40

References in corpus (21)

• Discovering the QCD Axion with Black Holes and Gravitational Waves
• Instability of the massive Klein-Gordon field on the Kerr spacetime
• Higher order WKB formula for quasinormal modes and grey-body factors: recipes for quick and accurate calculations
• Black holes in galaxies: environmental impact on gravitational-wave generation and propagation
• Black hole superradiance of self-interacting scalar fields
• The Spectra of Gravitational Atoms
• Bosenova collapse of axion cloud around a rotating black hole
• Disks, spikes, and clouds: distinguishing environmental effects on BBH gravitational waveforms
• Stability of highly-charged Reissner-Nordström black holes to charged scalar perturbations
• Quasibound states of Schwarzschild acoustic black holes
• Dicke superradiance in ordered lattices: dimensionality matters
• Correspondence between grey-body factors and quasinormal frequencies for rotating black holes
• Analytic expressions for quasinormal modes and grey-body factors in the eikonal limit and beyond
• Black hole jets on the scale of the Cosmic Web
• Black hole superradiance with (dark) matter accretion
• Instability of the charged massive scalar field on the Kerr-Newman black hole spacetime
• Black hole superradiant instability for massive spin-2 fields
• Superradiant Instability of Magnetic Black Holes
• Next-to-leading-order solution to Kerr-Newman black hole superradiance
• Effects of Superradiance in Active Galactic Nuclei
• Self-interaction effects on the Kerr black hole superradiance and their observational implications