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

TL;DR

This paper introduces and analyzes position-dependent mass Klein-Gordon oscillators in cosmic string spacetime within Kaluza-Klein theory, exploring their spectra, confinement properties, and non-Hermitian extensions under magnetic and Aharonov-Bohm flux fields.

Contribution

It presents new models of PDM Klein-Gordon oscillators in cosmic string spacetime within Kaluza-Klein theory, including confinement effects and non-Hermitian PT-symmetric extensions.

Findings

Spectral analysis under different parametric effects

Identification of PDM KG-oscillators with Cornell-type confinement

Extension to non-Hermitian PT-symmetric Coulombic models

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 $\mathcal{PT}$-symmetric PDM-Coulombic-type KG-particle model in cosmic string spacetime within KKT14