On the gravitational coupling of Klein–Gordon particles to matter vorticity and spacetime torsion: Vorticity–energy correlations and isospectrality

We consider Klein–Gordon (KG) particles in a Gödel-type universe in cosmic string spacetime within a non-minimal coupling field [Formula: see text], where [Formula: see text]. In the limit [Formula: see text], the non-minimal coupling field retrieves the KG oscillators in the Som–Raychaudhuri cosmic string spacetime. This assumption provides conditional/quasi-exact solvability through confluent Heun polynomials [Formula: see text] for KG particles in Gödel-type cosmic string spacetime and the non-minimal coupling field [Formula: see text]. Moreover, it allows exact solvability for the case [Formula: see text] due to the correlation between the confluent Heun polynomials [Formula: see text] and the hypergeometric polynomials [Formula: see text]. In both cases ([Formula: see text] and [Formula: see text]), we show that the radial wave functions satisfy the quantum mechanical conditions of finiteness (including [Formula: see text] and [Formula: see text]) and square integrability. We also explore and report isospectralities associated with two Gödel-type cosmic string spacetimes characterized by opposite matter vorticities, [Formula: see text] and [Formula: see text], where vorticity–energy correlations are consequently reported. To the best of our knowledge, only Figueiredo et al. [9] have discussed the case [Formula: see text]. Therefore, the methodology and results of this study have not been published elsewhere.