The Klein-Gordon-Fock equation in the curved spacetime of the Kerr-Newman (anti) de Sitter black hole

Understand

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.