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 Schrodinger-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) g(0)(y)= 1, g(1)(y)= root 1- epsilon y(2), (b) g(0)(y)= 1, g(1)( y)= root 1- epsilon y, (c) g(0)(y)= g(1) (y)=(1- epsilon y) (1), and (d) g(0)( y) =(e(epsilon y)- 1)/epsilon y, g(1)(y)= 1. Interestingly, we observe that the first pair in (a) introduces the Planck energy Epas a maximum possible KG-particle/antiparticle energy value. (c) 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP(3).
