Scalar Perturbation Around Rotating Regular Black Hole: Superradiance Instability and Quasinormal Modes

Black holes provide a natural laboratory to study particle physics and astrophysics. When black holes are surrounded by matter fields, there will be plenty of phenomena which can have observational consequences, from which we can learn about the matter fields as well as black hole spacetime. In this work, we investigate the massive scalar field in the vicinity of a newly proposed rotating regular black hole inspired by quantum gravity. We will especially investigate how this non-singular spactime will affect the superradiance instability and quasinormal modes of the scalar filed. We derive the superradiant conditions and the amplification factor by using the Matching-asymptotic Method, and the quasinormal modes are computed through Continued Fraction Method. In the Kerr limit, the results are in excellent agreements with previous research. We also demonstrate how the quasinormal modes will change as a function of black hole spin, regularity described by a parameter $k$ and scalar field mass respectively, with other parameters taking specific values.