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 when a regularization parameter is introduced through loop quantum corrections. This parameter is expected to give rise to 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, we obtain the waveform of massless scalar fields evolving over time. By analyzing the waveform, we find that the regularization parameter only affects the damping oscillation of waveform, but not the initial outburst and late-time tail stages. This behavior is characterized by quasi-normal modes. Under scalar field perturbations, the loop quantum black holes remain stable. Moreover, we calculate the quasi-normal modes of massive scalar fields by three numerical methods, which are the Prony, WKB, and shooting methods, respectively. Our results indicate that the real part of quasi-normal modes depends only on the regularization parameter, while the imaginary part does not only on the regularization parameter but also on the angular momentum. Finally, we study the amplification effect of rotating black holes, i.e., the superradiance. Our analyses indicate the existence of stronger superradiance around loop quantum gravity black holes compared to Kerr ones.