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

TL;DR

This paper investigates the effects of loop quantum gravity corrections on scalar fields around rotating black holes, revealing impacts on waveform damping, quasi-normal modes, stability, and enhanced superradiance compared to classical Kerr black holes.

Contribution

It provides the first detailed analysis of scalar waveforms, quasi-normal modes, and superradiance in rotating loop quantum gravity black holes, highlighting the influence of the regularization parameter.

Findings

Regularization parameter affects waveform damping but not initial outburst or late-time tail.

Loop quantum gravity black holes remain stable under scalar perturbations.

Superradiance is stronger around loop quantum gravity black holes than Kerr black holes.

Abstract

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.