Confined Klein-Gordon oscillator from a (2+1)-dimensional G\"{u}rses to a G\"{u}rses or a pseudo-G\"{u}rses space-time backgrounds: Invariance and isospectrality

TL;DR

This paper investigates the exact solutions of the Klein-Gordon oscillator with Cornell confinement in (2+1)-dimensional G"{u}rses space-times, revealing effects of vorticity on energy levels and demonstrating invariance and isospectrality across different space-time backgrounds.

Contribution

It introduces exact solutions for the KG oscillator in G"{u}rses backgrounds, analyzing vorticity effects and establishing invariance and isospectrality in deformed and different space-time geometries.

Findings

Vorticity parameter causes energy level crossings and clustering.

Energy gap shifts due to vorticity and deformation.

Invariance and isospectrality between different space-time backgrounds.

Abstract

We study the Klein-Gordon (KG) oscillator with a Cornell-type scalar confinement in (2+1)-dimensional G\"{u}rses 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 G\"{u}rses space-time background. Moreover, we consider the confined-deformed KG-oscillator from a (2+1)-dimensional G\"{u}rses to G\"{u}rses and pseudo-G\"{u}rses space-time backgrounds. The resulting confined-deformed KG-oscillators are found to admit invariance and isospectrality with each other