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

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 $y=E\mathrm{/}{E}_P$, 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}, © $g_{{}_0}\left(y\right)=g_{{}_1}\left(y\right)={(1-\epsilon y)}^{-1}$, and (d) $g_{{}_0}(y)=(e^{\epsilon y}-1)\mathrm{/}\epsilon y$, $g_{{}_1}\left(y\right)=1$. Interestingly, we observe that the first pair in (a) introduces the Planck energy $E_p$ as a maximum possible KG-particle/antiparticle energy value.