Relativistic motions of spin-zero quantum oscillator field in a global monopole space-time with external potential and AB-effect

In this paper, we analyze a spin-zero relativistic quantum oscillator in the presence of the Aharonov–Bohm magnetic flux in a space-time background produced by a point-like global monopole (PGM). Afterwards, we introduce a static Coulomb-type scalar potential and subsequently with the same type of vector potential in the quantum system. We solve the generalized Klein–Gordon oscillator analytically for different functions (e.g. Coulomb- and Cornell-type functions) and obtain the bound-states solutions in each case. We discuss the effects of topological defects associated with the scalar curvature of the space-time and the Coulomb-type external potentials on the energy profiles and the wave function of these oscillator fields. Furthermore, we show that the obtained energy eigenvalues depend on the magnetic quantum flux which gives rise to the gravitational analogue of the Aharonov–Bohm (AB) effect.