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We apply the confluent Heun functions to study the resonant frequencies(quasispectrum), the Hawking radiation and the scattering process of scalarwaves, in a class of spacetimes, namely, the ones generated by aKerr-Newman-Kasuya spacetime (dyon black hole) and a Reissner-Nordstr\"{o}mblack hole surrounded by a magnetic field (Ernst spacetime). In bothspacetimes, the solutions for the angular and radial parts of the correspondingKlein-Gordon equations are obtained exactly, for massive and massless fields,respectively. The special cases of Kerr and Schwarzschild black holes areanalyzed and the solutions obtained, as well as in the case of a Schwarzschildblack hole surrounded by a magnetic field. In all these special situations, theresonant frequencies, Hawking radiation and scattering are studied.

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