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

Abstract

We investigate Klein-Gordon (KG) oscillators in a Gö% del-type Som-Raychaudhuri spacetime in a mixed magnetic field (given by the vector potential $A_{μ}=\left( 0,0,A_{φ},0\right) $, with $% A_{φ}=B_{1}r^{2}/2+B_{2}r$). The resulting KG equation takes a Schr% ödinger-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( α,β,γ,δ,z\right) $% . The usual power series expansion of which is truncated to a polynomial of \ order $n_{r}+1=n\geq 1$ through the usual condition $γ=2\left( n_{r}+1\right) +α$. However, we use the very recent recipe suggested by Mustafa \cite{1.29} as an alternative parametric condition/correlation. i.e., $δ=-β\left( 2n_{r}+α+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.