The Dirac equation in a class of topologically trivial flat Gödel-type space-time backgrounds

In this work, we investigate the behaviour of Dirac particles in a class of Gödel-type space-time backgrounds in the presence of non-minimal coupling of the gravitational field with background curvature. We obtain the allowed energies for this relativistic system by solving analytically the Dirac equation in flat and curved space in a topologically trivial flat Gödel-type metric, and analyze the effects on the energy eiegnvalues.