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

TL;DR

This paper studies Klein-Gordon oscillators in a G"odel-type Som-Raychaudhuri spacetime with a mixed magnetic field, deriving exact solutions using Heun functions and exploring how the spacetime and magnetic field influence the oscillator's spectrum.

Contribution

It introduces a novel parametric condition for solving KG-oscillators in this spacetime, enabling exact solutions and analyzing the effects of magnetic fields and spacetime rotation on the spectrum.

Findings

Exact solutions obtained using Heun functions.

Magnetic field and spacetime rotation significantly affect the spectrum.

Conditional exact solvability achieved through a new parametric condition.

Abstract

We investigate Klein-Gordon (KG) oscillators in a G\"{o}% del-type Som-Raychaudhuri spacetime in a mixed magnetic field (given by the vector potential $A_{\mu }=\left( 0,0,A_{\varphi },0\right) $, with $% A_{\varphi }=B_{1}r^{2}/2+B_{2}r$). The resulting KG equation takes a Schr% \"{o}dinger-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 $n_{r}+1=n\geq 1$ 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 G\"{o}del-type SR-spacetime background on the KG-oscillators' spectroscopic structure.