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 $A_{\mu }=\left(0,0,A_{\phi },0\right)$, with ). 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 $H_B\left(\alpha ,\beta ,\gamma ,\delta ,z\right)$% . 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 \cite{1.29} as an alternative parametric condition/correlation. i.e., $\delta =-\beta \left(2n_r+\alpha +3\right)$, 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.

10 pages, 2 figures

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