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

Abstract

In this paper, we discuss Klein-Gordon (KG) oscillators in the (1+2)-dimensional Gurses spacetime and under position-dependent mass (PDM) settings. We observe that the KG Gurses oscillators are introduced as a byproduct of the very nature of the Gurses spacetime structure. We report that the energy levels of such KG Gurses oscillators admit vorticity-energy correlations as well as spacetime-associated degeneracies (STADs). Moreover, we introduce a new set of KG pseudo-Gurses oscillators that admits isospectrality and invariance with the KG Gurses oscillators and inherits the same vorticity-energy correlations as well as STADs.