PDM Klein–Gordon particles in Gödel-type Som–Raychaudhuri cosmic string spacetime background

In G\"odel-type Som-Raychaudhuri (SR) cosmic string spacetime background, we re-cycle the Klein-Gordon (KG) oscillators and report their correct exact solutions. We argue that mathematical collapse of KG-equation into 2-dimensional radial Schr\"odinger-like oscillator does not yield parametric characterizations one is inherited by other. The angular frequency (positive) in Schr\"odinger case replaced an irrational frequency-like (positive negative) KG-case. Inheriting oscillator's implies at least half spectra (the negative part) lost process. also introduce KG-oscillators pseudo-G\"odel SR-type admit invariance isospectrality with those G\"odel background. position-dependent mass (PDM) settings to KG-particles 4-vector scalar Lorentz potentials magnetic field Four illustrative examples fundamental nature are discussed or conditionally solvability reported. Amongst are, a PDM KG-Coulombic particle Coulombic field, zero vorticity, equally mixed quasi-free KG-oscillator. emphasis biconfluent Heun polynomial approach, effective plus Cornell type potential, yields paralyzes solution from collapsing pure one.