On the Klein–Gordon scalar field oscillators in a spacetime with spiral-like dislocations in external magnetic fields

We investigate the effects of two types of spiral dislocation (the distortion of the radial line, labeled as spiral dislocation I, and the distortion of a circle, labeled as spiral dislocation II) on the relativistic dynamics of the Klein–Gordon (KG) oscillator fields, both in the presence and absence of external magnetic fields. In this context, our investigations show that while spiral dislocation I affects the energies of the KG oscillators (with or without the magnetic field), spiral dislocation II has, interestingly, no effect on the KG oscillator's energies unless a magnetic field is applied. However, for both types of spiral dislocations, we observe that the corresponding wave functions incorporate the effects of the dislocation parameter. Our findings are based on the exact solvability and conditional exact solvability (associated with the biconfluent Heun polynomials) of the KG oscillators (with or without the magnetic field, respectively) for spiral dislocation I, and the exact solvability of the KG oscillators (with or without the magnetic field) for spiral dislocation II. The exact solvability of the latter suggests that the oscillator's frequency is solely determined by the magnetic field strength.