Klein–Gordon particles in Gödel-type Som-Raychaudhuri cosmic string spacetime and the phenomenon of spacetime associated degeneracies

We argue that only exact, comprehensive, and explicit solutions for the fundamental models, Klein-Gordon (KG) oscillators KG-Coulomb, would help to understand effects of gravitational fields on dynamics such quantum mechanical systems. In current methodical proposal, generated by a G\"odel-type Som-Raychaudhuri (SR) cosmic string spacetime KG-oscillators (KG-particles in general) are studied reported. so doing, we revisit topologically trivial background use textbook procedures report its exact solution covers even odd parities. Next, discuss drawbacks associated with power series expansion approach implies biconfluent Heun functions/polynomials solution. We, therefore, recollect called pseudo perturbative shifted L technique (PSLET) as an alternative more sophisticated method/technique. Illustrative examples used: (i) KG-oscillator spacetime, (ii) quasi-free G\"odel SR-type (iii) KG-Coulombic particle at zero vorticity, (iv) massless KG-particle Cornell-type Lorentz scalar potential. The corresponding energies obtained from zeroth (leading) order correction PSLET, where all higher identically vanish. comprehensive exactness reported manifestly suggest degeneracies (STAD) phenomenon.