PDM KG-Coulombic particles in cosmic string rainbow gravity spacetime and a uniform magnetic field

TL;DR

This paper investigates Klein-Gordon particles in cosmic string rainbow gravity spacetime with a magnetic field, deriving exact solutions for energy levels and wave functions, and exploring effects of different rainbow functions on particle energies.

Contribution

It provides exact solutions for KG particles in rainbow gravity spacetime with magnetic fields, considering position-dependent mass and various rainbow functions, revealing the maximum energy limit set by Planck energy.

Findings

Exact solutions for KG-Coulombic particles obtained

Planck energy acts as a maximum energy limit in some models

Different rainbow functions influence particle energy spectra

Abstract

Klein-Gordon (KG) particles in cosmic string rainbow gravity spacetime and a uniform magnetic field are studied in the context of the so called, metaphorically speaking, position-dependent mass (PDM) settings. We show that the corresponding KG-equation collapses into a two-dimensional radial Schr\"{o}dinger-Coulomb like model. The exact textbook solution of which is used to find the energies and wave functions of KG-Coulombic particles (both constant mass and PDM ones). In so doing, we consider, with $y=E/E_{P}$, four pairs of rainbow functions: (a) $% g_{_{0}}\left( y\right) =1$, $g_{_{1}}\left( y\right) =\sqrt{1-\epsilon y^{2}% }$, (b) $g_{_{0}}\left( y\right) =1$, $g_{_{1}}\left( y\right) =\sqrt{% 1-\epsilon y}$, (c) $g_{_{0}}\left( y\right) =g_{_{1}}\left( y\right) =\left( 1-\epsilon y\right) ^{-1}$, and (d) $g_{_{0}}( y) =(e^{\epsilon y}-1) /\epsilon y$, $g_{_{1}}\left( y\right) =1$. Interestingly, we observe that the first pair in (a) introduces the Planck energy $E_{p}$ as a maximum possible KG-particle/antiparticle energy value.