Exact solutions of the Klein–Gordon equation in the Kerr–Newman background and Hawking radiation

Abstract

This work considers the influence of the gravitational field produced by a charged and rotating black hole (Kerr-Newman spacetime) on a charged massive scalar field. We obtain exact solutions of both angular and radial parts of the KleinGordon equation in this spacetime, which are given in terms of the confluent Heun functions. From the radial solution, we obtain the exact wave solutions near the exterior horizon of the black hole, and discuss the Hawking radiation of charged massive scalar particles.

Acoustic black holes: massless scalar field analytic solutions and analogue Hawking radiation

“…which is a result already formally obtained in the literature [55] in different context, and is analogous to the obtained in [61] for an astrophysical black hole. According to the Damour-Ruffini-Sannan method [62,63] for astrophysical black holes, a correct wave describing a particle flying off of the canonical acoustic black hole is given by …”

Variations in the fine-structure constant constraining gravity theories

“…It is important to call attention to the fact that all these discussions considered only approximate solutions to the problem. In fact, only recently the exact and complete solutions for the field dynamics of a scalar field in Schwarzschild spacetime was solved in [16,17] in terms of the Heun's functions due to advances on the study these functions in recent years.…”

“…In fact, the relative absorption probability of the scalar wave at the event horizon surface of a static and uncharged black hole is given by [16] …”

Hawking radiation and interacting fields

“…Recently, it has been shown how to solve exactly the Klein-Gordon equation in a KerrNewman geometry [21]. In this way, the authors were able to derive the Hawking radiation in a rather straightforward way using the technique devised by Ruffini and Damour [10] and Sannan [11].…”

“…All the standard machinery to derive Hawking radiation applies (e.g. see [21] or [5]). Looking for purely radial solutions (here φ = 0 and θ = π/2), we have…”