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

TL;DR

This paper introduces an exact method using confluent Heun functions to compute radiation fluxes from perturbations in type-D black holes, improving accuracy and efficiency over previous approximation methods.

Contribution

The authors develop a novel exact solution approach for Teukolsky equations using confluent Heun functions, applicable to any perturbation fields of type-D black holes.

Findings

Exact solutions are derived without constraints like low-frequency or weak-field.

The method improves computational accuracy over previous approximation techniques.

Applications to Schwarzschild black holes validate the approach.

Abstract

We present a novel method that solves Teukolsky equations with the source to calculate radiation fluxes at infinity and event horizon for any perturbation fields of type-D black holes. For the first time, we use the confluent Heun function to obtain the exact solutions of ingoing and outgoing waves for the Teukolsky equation. This benefits from our derivation of the asymptotic analytic expression of the confluent Heun function at infinity. It is interesting to note that these exact solutions are not subject to any constraints, such as low-frequency and weak-field. To illustrate the correctness, 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 improves the computational accuracy and efficiency compared with the 23rd post-Newtonian order expansion and the Mano-Suzuki-Takasugi method.