Relativistic quantum dynamics of scalar particles in the rainbow formalism of gravity

In the present article, we investigate the Klein–Gordon equation (KGE) in a topologically trivial Gödel-type space-time in the context of rainbow gravity (RG). Exact solutions and energy spectrum of scalar particles are obtained for the considered model. Also, the same systems are studied with the existence of the Klein–Gordon oscillator (KGO) potential. Results are evaluated by considering two different rainbow functions and they are analyzed graphically. We observe that the energy spectrum of scalar particles is modified by rainbow functions compared to the solutions obtained via the ordinary general relativity (GR) theory. (paper)