Position dependent mass (PDM) Klein–Gordon scalar particles in Bonnor-Melvin-Lambda space-time

Abstract

In this paper, we investigate Klein–Gordon scalar particles featuring a position-dependent mass within the framework of a cosmological space-time, specifically a four-dimensional Bonnor-Melvin magnetic solution incorporating a cosmological constant. The radial wave equation for the scalar multiplier \(m=m(r)\) is derived utilizing an appropriate wave function ansatz. We proceed to solve this radial equation for three distinct scalar multipliers: (i) \(m(r)=m_0\,e^{\frac{1}{2}\,\beta \,r^2}\), (ii) \(m(r) \propto r^{\alpha }\), and (iii) \(m(r)=m_0\,e^{\xi \,r}\), where \(\alpha \ge 0, \beta \ge 0, \xi \ge 0\). The resulting energy levels and wave functions for spin-0 scalar particles are shown to be influenced by the cosmological constant and the geometrical topology generating an angular deficit. Furthermore, we observe modifications in the energy levels compared to the Landau levels obtained in a flat space, highlighting the intricate interplay between position-dependent mass, cosmological factors, and the underlying space-time topology.