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We present a novel method that solves Teukolsky equations with the source tocalculate radiation fluxes at infinity and event horizon for any perturbationfields of type-D black holes. For the first time, we use the confluent Heunfunction to obtain the exact solutions of ingoing and outgoing waves for theTeukolsky equation. This benefits from our derivation of the asymptoticanalytic expression of the confluent Heun function at infinity. It isinteresting to note that these exact solutions are not subject to anyconstraints, such as low-frequency and weak-field. To illustrate thecorrectness, we apply these exact solutions to calculate the gravitational,electromagnetic, and scalar radiations of the Schwarzschild black hole.Numerical results show that the proposed exact solution appreciably improvesthe computational accuracy and efficiency compared with the 23rd post-Newtonianorder expansion and the Mano-Suzuki-Takasugi method.

Radiation fluxes of gravitational, electromagnetic, and scalar perturbations in type-D black holes: an exact approach