The Klein–Gordon equation in the spacetime of a charged and rotating black hole

This work deals with the influence of the gravitational field produced by a charged and rotating black hole (Kerr-Newman spacetime) on massive scalar fields. We obtain an exact solution of the Klein-Gordon equation in this spacetime, which is given in terms of the confluent Heun functions. In the particular case corresponding to an extreme Kerr-Newman black hole the solution is given by the double confluent Heun functions. We also investigate the solutions in regions near the event horizon and far from the black hole.