On Klein–Gordon Gürses oscillators and pseudo-Gürses oscillators: Vorticity–energy correlations and spacetime-associated degeneracies

Abstract

In this paper, we discuss Klein–Gordon (KG) oscillators in the [Formula: see text]-dimensional Gürses spacetime and under position-dependent mass (PDM) settings. We observe that the KG Gürses oscillators are introduced as a byproduct of the very nature of the Gürses spacetime structure. We report that the energy levels of such KG Gürses oscillators admit vorticity–energy correlations as well as spacetime-associated degeneracies (STADs). Moreover, we introduce a new set of KG pseudo-Gürses oscillators that admits isospectrality and invariance with the KG Gürses oscillators and inherits the same vorticity–energy correlations as well as STADs.