Klein–Gordon equation in the presence of a vector generalized Yukawa and a scalar generalized Hulthen potentials in the rotating cosmic string space–time

In this paper, we explore the relativistic quantum dynamics of spin-0 oscillator fields within the framework of a rotating cosmic string space–time, taking into account the presence of scalar and vector potentials. We solve the Klein–Gordon oscillator equation in this curved space–time, incorporating generalized versions of the Yukawa and Hulthen potentials as vector and scalar potentials, respectively. The analytical solution of the quantum system yields the energy eigenvalue and corresponding eigenfunction, which is expressed in terms of confluent Heun functions. The resulting energy spectrum is shown to depend on various parameters associated with the cosmic string space–time and the confining potentials. We graphically illustrate how the energy spectrum varies with changes in both the potential parameters and the cosmic string parameters.