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

TL;DR

This paper employs confluent Heun functions to derive exact solutions for scalar wave phenomena around various black hole spacetimes, providing insights into their resonant frequencies, Hawking radiation, and scattering processes.

Contribution

It introduces a novel application of confluent Heun functions to obtain exact solutions for scalar wave equations in complex black hole backgrounds, including Kerr-Newman-Kasuya and Ernst spacetimes.

Findings

Exact solutions for angular and radial equations in specified spacetimes.

Determination of resonant frequencies and Hawking radiation characteristics.

Analysis of scattering processes for scalar waves in these black hole environments.

Abstract

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-Nordstr\"{o}m 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.