Analytic treatment of the system of a Kerr-Newman black hole and a charged massive scalar field

Abstract

Charged rotating Kerr-Newman black holes are known to be superradiantly unstable to perturbations of charged massive bosonic fields whose proper frequencies lie in the bounded regime $0<\omega <\text{min}\{{\omega }_{\text{c}}\equiv m{\Omega }_{\text{H}}+q{\Phi }_{\text{H}},\mu \}$ [here $\{{\Omega }_{\text{H}},{\Phi }_{\text{H}}\}$ are respectively the angular velocity and electric potential of the Kerr-Newman black hole, and $\{m,q,\mu \}$ are respectively the azimuthal harmonic index, the charge coupling constant, and the proper mass of the field]. In this paper we study analytically the complex resonance spectrum which characterizes the dynamics of linearized charged massive scalar fields in a near-extremal Kerr-Newman black-hole spacetime. Interestingly, it is shown that near the critical frequency ${\omega }_{\text{c}}$ for superradiant amplification and in the eikonal large-mass regime, the superradiant instability growth rates of the explosive scalar fields are characterized by a non-trivial (non-monotonic) dependence on the dimensionless charge-to-mass ratio $q/\mu$. In particular, for given parameters $\{M,Q,J\}$ of the central Kerr-Newman black hole, we determine analytically the optimal charge-to-mass ratio $q/\mu$ of the explosive scalar field which {\it maximizes} the growth rate of the superradiant instabilities in the composed Kerr-Newman-black-hole-charged-massive-scalar-field system.

11 pages

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• Next-to-leading-order solution to Kerr-Newman black hole superradiance
• Massive Scalar Perturbation of Extremal Rotating Braneworld Black hole: Superradiant Stability Analysis
• The fastest relaxation rate of higher-dimensional Reissner--Nordström black hole
• Relaxation rate of RNdS black hole
• Hawking temperature of black holes with multiple horizons
• The superradiant stability of Kerr-Newman black holes
• Black Hole Superradiance in f(R) Gravities
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