Novel Spectroscopy of Non-commutative Geometry Inspired Kerr Black Hole: Black Hole Bomb, Scalar Cloud, Resonant Scattering

We investigate scalar field dynamics in a noncommutative Kerr black hole spacetime, constructed from the static noncommutative Schwarzschild solution via the Newman–Janis algorithm. The covariant Klein–Gordon equation is shown to be fully separable, yielding spheroidal harmonics in the angular sector and exact radial solutions in terms of confluent Heun functions. Using the exact solution, we derive the quasibound state spectrum and obtain an analytic description of the ultralight (gravitational atom) regime through a systematic expansion of the complex frequency. The real part of the spectrum exhibits a hydrogenic structure with corrections arising from rotation and noncommutativity, while the imaginary part determines the stability properties of the modes. We show that superradiant instability arises for co-rotating modes when the rotational contribution exceeds the binding energy, whereas counter-rotating modes remain purely damped. Noncommutative effects enter through the parameter Θ, effectively enhancing the rotational coupling, shifting the instability threshold, and modifying the associated growth rates. We further analyze scalar superradiant scattering using the analytical asymptotic matching method in the low-frequency, slow-rotation regime. Within this framework, we derive analytic expressions for both the amplification factor and the greybody factor. We show that superradiance occurs only for Ω < mlΩH. Our results demonstrate that increasing Θ enhances the amplification, widens the superradiant window, and modifies the decay rate in the non-superradiant regime.