Exact solutions of the Klein–Gordon equation in the Kerr–Newman background and Hawking radiation

•The covariant Klein–Gordon equation for a charged massive scalar field in the Kerr–Newman black hole is solved.•Both angular and radial parts are transformed to a Heun-type equation.•The resulting Hawking radiation spectrum of scalar particles has a thermal character.

This work considers the influence of the gravitational field produced by a charged and rotating black hole (Kerr–Newman spacetime) on a charged massive scalar field. We obtain exact solutions of both angular and radial parts of the Klein–Gordon equation in this spacetime, which are given in terms of the confluent Heun functions. From the radial solution, we obtain the exact wave solutions near the exterior horizon of the black hole, and discuss the Hawking radiation of charged massive scalar particles.