KG-oscillators in a spinning cosmic string spacetime and an external magnetic field

Abstract

We study the Klein-Gordon (KG) oscillators in a spinning cosmic string spacetime and an external magnetic field. The corresponding KG-equation is shown to admit a solution in the form of the confluent hypergeometric functions/polynomials. Consequently, the corresponding energies are shown to be given in a quadratic equation of delicate nature that has to be solved in an orderly manner (for it involves the energies for KG-particles/antiparticles, $E=E_{\pm }=\pm \left|E\right|$ along with the magnetic quantum number $m=m_{\pm }=\pm \left|m\right|$). Following a case-by-case strategy allowed us to clearly observe the effects of the spinning cosmic string on the spectroscopic structure of the KG-oscillators. Interestingly, we have observed that the coexistence of a spinning cosmic string and an external magnetic field eliminates the effect of the wedge parameter for KG-particles ($E=E_{+}$), with $m=m_{+}$, but not for the KG-antiparticles ($E=E_{-}$), with $m=m_{-}$. Such coexistence is observed to break the symmetry of the energies of the KG-particles and the antiparticles about $E=0$ for the KG-oscillators. However, for KG-particles ($E=E_{+}$), with $m=m_{-}$, and KG-antiparticles ($E=E_{-}$), with $m=m_{+}$, they are found to be unfortunate because they are indeterminable. Moreover, for the spinning parameter $\beta >>1$, the clustering of the energy levels is observed eminent to indicate that there is no distinction between energy levels at such values of β.