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 $A_{\mu }=(0,0,A_{\phi },0)$, 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 $H_B(\alpha ,\beta ,\gamma ,\delta ,z)$. The usual power series expansion of which is truncated to a polynomial of order $n_r+1=n\ge 1$ through the usual condition $\gamma =2(n_r+1)+\alpha$. However, we use the very recent recipe suggested by Mustafa [42] as an alternative parametric condition/correlation. i.e., $\delta =-\beta (2n_r+\alpha +3)$, 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.