KG- oscillators in Som-Raychaudhuri rotating cosmic string spacetime in a mixed magnetic field

We investigate Klein-Gordon (KG) oscillators in a Gödel-type Som-Raychaudhuri spacetime in a mixed magnetic field (given by the vector potential ${A}_{\mu }=\left(0,0,{A}_{\phi },0\right)$, with ${A}_{\phi }={B}_{1}{r}^{2}/2+{B}_{2}r$). The resulting KG equation takes a Schrödinger-like form (with an oscillator plus a linear plus a Coulomb-like interactions potential) that admits a solution in the form of biconfluent Heun functions/series ${H}_{B}\left(\alpha ,\beta ,\gamma ,\delta ,z\right)$. The usual power series expansion of which is truncated to a polynomial of order ${n}_{r}+1=n\ge 1$ through the usual condition $\gamma =2\left({n}_{r}+1\right)+\alpha $. However, we use the very recent recipe suggested by Mustafa [42] as an alternative parametric condition/correlation. i.e., $\delta =-\beta \left(2{n}_{r}+\alpha +3\right)$, to facilitate conditional exact solvability of the problem. We discuss and report the effects of the mixed magnetic field as well as the effects of the Gödel-type SR-spacetime background on the KG-oscillators' spectroscopic structure.