Confluent Heun functions and the physics of black holes: Resonant frequencies, Hawking radiation and scattering of scalar waves

• Charged massive scalar field in the dyon black hole and massless scalar field in the Ernst spacetime are analyzed.
• The confluent Heun functions are applied to obtain the solution of the Klein–Gordon equation.
• The resonant frequencies are obtained.
• The Hawking radiation and the scattering process of scalar waves are examined.

We apply the confluent Heun functions to study the resonant frequencies (quasispectrum), the Hawking radiation and the scattering process of scalar waves, in a class of spacetimes, namely, the ones generated by a Kerr–Newman–Kasuya spacetime (dyon black hole) and a Reissner–Nordström black hole surrounded by a magnetic field (Ernst spacetime). In both spacetimes, the solutions for the angular and radial parts of the corresponding Klein–Gordon equations are obtained exactly, for massive and massless fields, respectively. The special cases of Kerr and Schwarzschild black holes are analyzed and the solutions obtained, as well as in the case of a Schwarzschild black hole surrounded by a magnetic field. In all these special situations, the resonant frequencies, Hawking radiation and scattering are studied.