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, effectively 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-Coulomb particles (both constant mass and PDM ones). In so doing, we consider, with y=E/EP, four pairs of rainbow functions: (a) g0(y)=1, g1(y)=1−ϵy2, (b) g0(y)=1, g1(y)=1−ϵy, (c) g0(y)=g1(y)=(1−ϵy)−1, and (d) g0(y)=(eϵy−1)/ϵy, g1(y)=1. Interestingly, we observe that the first pair in (a) introduces the Planck energy Ep as a maximum possible KG-particle/antiparticle energy value.
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