Eur. Phys. J. Plus (2024) 139: 911
https://doi.org/10.1140/epjp/s13360-024-05706-x

Regular Article

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

¹ Department of Physics, University of Science and Technology Meghalaya, 793101, Ri-Bhoi, India
² Laboratory of Theoretical and Applied Physics, Echahid Cheikh Larbi Tebessi University, 12001, Tebessa, Algeria

^b abdelmalekbouzenada@gmail.com

Received: 18 December 2023
Accepted: 1 October 2024
Published online: 21 October 2024

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.