Confined Klein–Gordon oscillator from a (2+1)-dimensional Gürses to a Gürses or a pseudo-Gürses space-time backgrounds: Invariance and isospectrality

We study the Klein–Gordon (KG) oscillator with a Cornell-type scalar confinement in (2+1)-dimensional Gürses space-time backgrounds and report their exact solutions. The effect of the vorticity parameter $\Omega $ on the energy levels is found to yield some interesting features like; energy levels-crossings, partial clustering of positive and negative energy levels, and shifting the energy gap upwards or downwards. Such confined KG-oscillators are also studied in a general deformed Gürses space-time background. Moreover, we consider the confined-deformed KG-oscillator from a (2+1)-dimensional Gürses to Gürses and pseudo-Gürses space-time backgrounds. The resulting confined-deformed KG-oscillators are found to admit invariance and isospectrality with each other.