PDM KG-oscillators in cosmic string rainbow gravity spacetime in a non-uniform magnetic field

TL;DR

This paper investigates how rainbow gravity and position-dependent mass influence Klein-Gordon oscillators in a cosmic string spacetime, revealing specific effects on energy spectra and emphasizing the maximum energy limit set by Planck scale.

Contribution

It introduces a detailed analysis of PDM Klein-Gordon oscillators within rainbow gravity in cosmic string spacetime, considering various rainbow functions and their impact on energy levels.

Findings

Rainbow functions significantly affect energy spectra.

Planck energy acts as maximum for KG-particles in certain cases.

PDM modifies the oscillator behavior in curved spacetime.

Abstract

We consider position-dependent mass (PDM) Klein-Gordon (KG) particles in cosmic string rainbow gravity spacetime in a non-uniform magnetic field. The corresponding KG-equation is reduced into the one-dimensional form of the two-dimensional radial Schr\"{o}dinger-oscillator like equation (hence the notion KG-oscillator). We first report on the effects of rainbow gravity on the energy levels of KG-oscillators with constant mass. Next, we include the PDM settings so that KG-oscillators like interaction are introduced. The effects of PDM on the spectra of KG-oscillators in cosmic string rainbow gravity spacetime are also reported. In both cases four pairs of rainbow functions are considered: (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) $g_{_{0}}\left( y\right) =\left( e^{\epsilon y}-1\right) /\epsilon y$, $g_{_{1}}\left( y\right) =1$, where $y=E/E_p$ and $\epsilon$ is the rainbow parameter. We report that, as long as KG-particles are in point, the rainbow functions pair in (a) is the only pair to emphasis that the Planck energy is the maximum possible energy the KG-particles may have.