Quantum effects in Reissner-Nordstr\"{o}m black hole surrounded by magnetic field: the scalar wave case

TL;DR

This paper investigates scalar wave phenomena such as resonant frequencies, Hawking radiation, and scattering in various black hole spacetimes, including those with magnetic fields, using exact solutions of the Klein-Gordon equation with confluent Heun functions.

Contribution

It provides exact solutions for scalar wave equations in complex black hole spacetimes, extending previous analyses to include magnetic field effects and special cases like Kerr and Schwarzschild black holes.

Findings

Exact solutions for scalar wave equations in dyon and Ernst spacetimes.

Analysis of resonant frequencies, Hawking radiation, and scattering in these spacetimes.

Extension of solutions to special cases like Kerr and Schwarzschild black holes.

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.