Resonance of Gravitational Axion-like Particles

The motion of gravitational axion-like particles (ALPs) around a Kerr black hole is analyzed, paying attention to the resonance and distribution of spectral radiation. We first discuss the computation of gR˜μνρρσRμνρσ and its implications with Pontryagin’s theorem, and then a detailed analysis of Teukolsky’s master equation is carried out. After carefully analyzing the Teukolsky master equation, we show that this system exhibits resonance when ω≳μ, where μ is the mass of the ALP, while the homogeneous part of the solution exhibits the superradiance. A skew-normal distribution can approximate the energy distribution of the resonant modes, and we give explicit expressions for its lifetime.