Exact Solutions of the Klein-Gordon Equation in the Presence of a Dyon, Magnetic Flux and Scalar Potential in the Specetime of Gravitational Defects

Abstract

In this paper we analyse the relativistic quantum motion of a charged spin-0 particle in the presence of a dyon, Aharonov-Bohm magnetic field and scalar potential, in the spacetimes produced by an idealized cosmic string and global monopole. In order to develop this analysis, we assume that the dyon and the Aharonov-Bohm magnetic field are superposed to both gravitational defects. Two distinct configurations for the scalar potential, $S(r)$, are considered: $i)$ the potential proportional to the inverse of the radial distance, i.e., $S\propto1/r$, and $ii)$ the potential proportional to this distance, i.e., $S\propto r$. For both cases the center of the potentials coincide with the dyon's position. In the case of the cosmic string the Aharonov-Bohm magnetic field is considered along the defect, and for the global monopole this magnetic field pierces the defect. The energy spectra are computed for both cases and explicitly shown their dependence on the electrostatic and scalar coupling constants. Also we analyse scattering states of the Klein-Gordon equations, and show how the phase shifts depend on the geometry of the spacetime and on the coupling constants parameter.