Superradiant instability of area-quantized Kerr black hole with discrete reflectivity

Abstract Ultralight bosons can condense to form the so-called scalar clouds around rotating black holes (BHs) through superradiant instabilities. When quantum effects near the Planck scale of the event horizon are considered, the classical BH is replaced by an exotic compact object, such as an area-quantized BH. In this work, we examine the superradiant instabilities of massive scalar fields around area-quantized BHs. We model the frequency-dependent reflectivity function of area-quantized BHs for massive scalar fields, which reflects the distinctive selection property of these BHs for massive scalar fields. We then utilize this model to investigate the case that the scalar fields can be superradiated by area-quantized BHs. We find that the area quantization of BHs can affect the formation and effective radius, and suppress the total mass of scalar clouds. Especially, the energy gap of area-quantized BHs can break the growth continuity of scalar clouds between different modes. These are distinct from the case of classical BHs.