The generalized Klein-Gordon oscillator with position-dependent mass in a particular G\"{o}del-type space-time

TL;DR

This paper explores the relativistic quantum behavior of a generalized Klein-Gordon oscillator with position-dependent mass in G"odel-type space-time, analyzing how potentials and space-time parameters influence energy spectra.

Contribution

It introduces a novel analysis of the Klein-Gordon oscillator with position-dependent mass in G"odel-type space-time, including effects of Cornell and linear potentials on energy levels.

Findings

Energy spectra are modified by space-time parameters.

Position-dependent mass influences the oscillator's energy levels.

Potentials affect the relativistic quantum dynamics.

Abstract

The relativistic quantum dynamics of the generalized Klein-Gordon (KG) oscillator having position-dependent mass in the G\"{o}del-type space-time is investigated. We have presented the generalized KG oscillator in this space-time, and discussed the effect of Cornell potential and linear potential for our considered system. The modification from the parameters of position-dependent mass and characterizing the space-time for the energy spectrums are presented.