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In this paper, We analyze a spin-zero relativistic quantum oscillator in thepresence of the Aharonov-Bohm (AB) magnetic flux in a space-time backgroundproduced by a point-like global monopole (PGM). Afterward, we introduce astatic Coulomb-type scalar potential and subsequently with the same type ofvector potential in the quantum system. We solve the generalized Klein-Gordonoscillator analytically for different functions (e.g. Coulomb- and Cornell-typefunctions) and obtain the bound-states solutions in each case. We discuss theeffects of topological defects associated with the scalar curvature of thespace-time and the Coulomb-type external potentials on the energy profiles andthe wave function of these oscillator fields. Furthermore, we show that theobtained energy eigenvalues depend on the magnetic quantum flux which givesrise to the gravitational analog of the Aharonov-Bohm (AB) effect

Relativistic Motions of Spin-Zero Quantum Oscillator Field in a Global Monopole Space-Time with External Potential and AB-effect