Klein–Gordon oscillator under gravitational effects in a topologically charged Ellis–Bronnikov wormhole

In this paper, we investigate the phenomenon of a relativistic quantum oscillator in non-massive wormhole spacetime, known in the literature as Ellis–Bronnikov-type wormhole, for a spin-zero particle subjected to the effects of a scalar field. We have obtained analytically the bound state solutions and your respective energy spectrum. The energy profile of this scalar field is modified by the wormhole throat as well as the scalar coupling constant of curvature. In the second part of the work, we investigate how the energy spectrum for a spin-zero particle is modified by an Aharonov–Bohm geometric phase effect. We also built a graphical representation to try to visualize this modification generated by the magnetic flux constant.