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

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 Schrödinger-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) , $g_{_{1}}\left( y\right) =\sqrt{1-εy^{2}% }$, (b) $g_{{}_0}\left(y\right)=1$, $g_{_{1}}\left( y\right) =\sqrt{% 1-εy}$, (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.

14 pages, 8 figures. arXiv admin note: substantial text overlap with arXiv:2301.05464

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• Fermion-antifermion pairs in magnetized spacetime generated by a point source
• Investigating quantum criticality through charged scalar fields near the BTZ black hole horizon
• Bound and Scattering States in a Spacetime with Dual Topological Defects: Cosmic String and Global Monopole
• Cornell and Coulomb potentials in the double defect spacetime