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 Aμ=(0,0,Aφ,0), with Aφ=B1r2/2+B2r). 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 HB(α,β,γ,δ,z). The usual power series expansion of which is truncated to a polynomial of order nr+1=n≥1 through the usual condition γ=2(nr+1)+α. However, we use the very recent recipe suggested by Mustafa 42 as an alternative parametric condition/correlation. i.e., δ=−β(2nr+α+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.