Scalar fields around a rotating loop quantum gravity black hole: Waveform, quasi-normal modes and superradiance

The rotating loop quantum gravity black hole is a newly proposed non-singular black hole, which eliminates spacetime singularities owing to the introduction of a regular parameter through loop quantum corrections. This regular parameter leads to many observable effects. In this paper, the dynamical behavior of a scalar field near a rotating loop quantum gravity black hole is investigated. Given a small initial perturbation by a massless scalar field, we obtain the waveform of the massless scalar field evolving over time. By analyzing the waveform, we find that the regular parameter only affects the decaying oscillation of waveform, which is mainly described by quasi-normal modes. Moreover, we calculate the quasi-normal modes of a massive scalar field by three numerical methods, which are the Prony, WKB, and shooting methods, respectively. Our results indicate that the regular parameter has a significant influence on quasi-normal modes, but the loop quantum black holes remain stable under scalar field perturbations. Finally, we study the amplification effect of rotating loop quantum gravity black holes on scalar fields, i.e., the superradiance effect. Our results indicate the existence of stronger superradiance around loop quantum gravity black holes than that around Kerr ones.