Extremal Kerr–Newman black hole’s absence of charged scalar cloud

The current work looks at the quasibound states and scalar cloud of relativistic charged scalar fields in an intense Kerr–Newman black hole. The absence of numerical techniques for solving the Klein–Gordon equation in the presence of extremal black holes is a well-known issue. Due to the difficulties, the numerical study is forced to end at the near-extreme limit. We discover a new exact quasibound state solution in the extreme Kerr–Newman black hole in terms of the Double Confluent Heun function. A series termination condition (quantization formula) is obtained by imposing the polynomial conditions of the Double Confluent Heun function and quasibound state boundary conditions, i.e., an ingoing wave near the black hole’s horizon and vanishing asymptotically far away from the black hole. Using the obtained quantization formula, we investigate the existence of a charged scalar cloud’s resonance frequency and discover that it is inexistent in the extreme Kerr–Newman black hole spacetime.