PDM Klein–Gordon oscillators in cosmic string spacetime in magnetic and Aharonov–Bohm flux fields within the Kaluza–Klein theory

Abstract

In the cosmic string spacetime and within Kaluza–Klein theory (KKT) backgrounds (indulging magnetic and Aharonov-Bohm flux fields), we introduce and study position-dependent mass (PDM) Klein–Gordon (KG) oscillators. The effective PDM is introduced as a deformation/defect in the momentum operator. We show that there are four different ways to obtain KG-oscillator. Two of which are readily known and the other two are obtained as byproducts of PDM settings. Next, we provide a thorough analysis on the corresponding spectra under different parametric effects, including the curvature parameter’s effect. Such analysis is used as a reference/lead model which is used in the discussion of different PDM KG-oscillators models: a mixed power-law and exponential type PDM model that yields a pseudo-confined PDM KG-oscillator in cosmic string spacetime within KKT (i.e., the PDM KG-oscillators are confined in their own PDM manifested Cornell-type confinement), and a PDM KG-oscillator confined in a Cornell-type potential. Moreover, we extend our study and discuss a non-Hermitian PT-symmetric PDM-Coulombic-type KG-particle model in cosmic string spacetime within KKT.