PDM relativistic quantum oscillator in Einstein-Maxwell-Lambda space-time

In this paper, we study the relativistic dynamics of quantum oscillator fields within the context of a position-dependent mass (PDM) system in the background of a curved space-time. The chosen curved space-time is generated by a magnetic field incorporating a non-zero cosmological constant called Einstein-Maxwell-Lambda solution. To analyze PDM quantum oscillator fields, we introduce a modification into the Klein-Gordon equation by substituting the four-momentum vector p(mu) -> (p(mu) + i eta X-mu + iF(mu)), where various four-vectors are defined by X-mu = (0,r, 0, 0), F-mu = (0, F-r, 0, 0) with F-r = f '(r)/4f(r), and eta is the mass oscillator frequency. The radial wave equation for the modified Klein-Gordon equation is derived and subsequently solve for two distinct scalar multipliers: (i) f(r) = e(1/2 alpha r2) and (ii) f(r) = r(beta), where alpha >= 0 and beta >= 0. The resultant approximate energy levels and wave function for quantum oscillator fields are demonstrated to be influenced by the cosmological constant and the geometrical topology parameter which breaks the degeneracy of the energy spectrum. Furthermore, we observed noteworthy modifications in the approximate energy levels and wave function when compared to the results derived in the flat space.