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-Nordström 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. Confluent Heun functions and the physics of black holes2

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.

This work deals with the influence of the gravitational field produced by a charged and rotating black hole (Kerr-Newman spacetime) on massive scalar fields. We obtain an exact solution of the Klein-Gordon equation in this spacetime, which is given in terms of the confluent Heun functions. In the particular case corresponding to an extreme Kerr-Newman black hole the solution is given by the double confluent Heun functions. We also investigate the solutions in regions near the event horizon and far from the black hole.PACS numbers: 04.20.Jb, 04.70.Dy, 02.30.Gp of the Klein-Gordon equation in some gravitational fields as well as their consequences have been discussed in the literature [1,2,3,4,5,6,7,8,9,10,11,12].By the middle of 70's of last century, Rowan and Stephenson [5], solved the Klein-Gordon equation for a massive field in the Kerr-Newman spacetime. The obtained solutions are not valid for the whole spacetime, but only near the exterior horizon and at infinity, and are given in terms of Whittaker functions.Solutions to the Klein-Gordon equation for a charged massive scalar field in the Kerr-Newman spacetime were obtained by Wu and Cai [9]. They showed that the radial and angular equations correspond to a generalized spin-weighted spheroidal wave functions, in the non-extreme case. In this context, the general solutions in integral forms and in power series expansion were obtained and the appropriate forms of the equations suitable to study some problems of physical interest, as the ones concerning black hole evaporation, black hole radiation and scattering states, among others, were presented and their solutions given. In the extreme case, the solutions of the radial equation were written in power series expansion and some discussion presented.Another paper by Furuhashi and Nambu [13] presents solutions of the Klein-Gordon equation for a massive scalar field in Kerr-Newman spacetime. The solutions were considered very far from the exterior event horizon and near the black hole event horizon. In the first case, it was found that the solutions regular at infinity is given in terms of the confluent hypergeometric functions, and in the opposite situation, namelly, near the horizon, the solution is given in terms of the Gauss hypergeometric function. Therefore, the obtained solutions are valid in a restricted ranges.In our paper we obtain the exact solutions of the Klein-Gordon equation in the background under consideration, valid in the whole space which corresponds to the black hole exterior which means between the event horizon and infinity. In this sense, we extend the range in which the solutions are valid as compared with the ones obtained by Rowan and Stephenson [5]. They are given in terms of solutions of the Heun equations [14]. We also analyze the asymptotic behavior of the solutions and compared with the corresponding ones obtained by Rowan and Stephenson [5]. The solution of the Klein-Gordon equation for the extreme Kerr-Newman black hole is also obtained and is given by the double confluent Heun fu...

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Charged massive scalar fields are considered in the gravitational and electromagnetic field produced by a dyonic black hole with a cosmic string along its axis of symmetry. Exact solutions of both angular and radial parts of the covariant Klein-Gordon equation in this background are obtained, and are given in terms of the confluent Heun functions. The role of the presence of the cosmic string in these solutions is showed up. From the radial solution, we obtain the exact wave solutions near the exterior horizon of the black hole, and discuss the Hawking radiation spectrum and the energy flux.