Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Klein-Gordon-Fock equation in the curved spacetime of the
  Kerr-Newman (anti) de Sitter black hole   Exact solutions of the Klein-Gordon-Fock (KGF) general relativistic equation
that describe the dynamics of a massive, electrically charged scalar particle
in the curved spacetime geometry of a charged, rotating Kerr-Newman-(anti) de
Sitter black hole are investigated. In the general case of a rotating, charged,
cosmological black hole the solution of the KGF equation with the method of
separation of variables results in Fuchsian differential equations for the
radial and angular parts which contain more than three finite singularities and
thereby generalise the Heun differential equations (HE). For particular values
of the physical parameters (i.e mass of the scalar particle) these Fuchsian
equations reduce to Heun equations and the solutions are expressed in terms of
Heun functions. For other values of the parameters some of the extra singular
points are false singular points. We derive the conditions on the coefficients
of the generalised Fuchsian equation such that a singular point is a false
point. In such a case the exact solution of the Fuchsian equation can in
principle be simplified and expressed in terms of Heun functions. We also
derive the exact solutions of the radial and angular equations for a massive
scalar (charged) particle in the Kerr-Newman spacetime. The analytic solutions
are expressed in terms of confluent Heun functions. Moreover, we derived the
constraints on the parameters of the theory such that the solution simplifies
and expressed in terms of confluent Kummer hypergeometric functions. We also
investigate the radial solutions in the KN case in the regions near the event
horizon and far from the black hole. Finally, we construct several expansions
of the solutions of the HE in terms of generalised hypergeometric functions of
Lauricella-Appell.

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The categories of this paper are: cs
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The categories of this paper are: hep-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: physics
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The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: atom-ph
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The categories of this paper are: econ
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The categories of this paper are: quant-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ex
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The categories of this paper are: math-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: stat