Linear confinement of a scalar and spin-0 particle in a topologically trivial flat Gödel-type space-time

Abstract In the previous work (Ahmed, Eur Phys J C 78(7):598, 2018), we investigated the relativistic quantum effects on a scalar and spin-half particles in a topologically trivial flat Gödel-type space-time. We have found that the energy eigenvalues of the system are influenced by the vorticity parameter characterizing the space-time. In the present work, we investigate the linear confinement of a scalar particle on the Klein–Gordon equation with a linear and Coulomb-type scalar potential in this flat Gödel-type solution. The energy eigenvalues of the system get modifies due to the presence of scalar potentials, and the vorticity parameter. In addition, we study the relativistic quantum motion of spin-0 particles with vector and scalar potentials of Coulomb-type and analyze the effects on the energy eigenvalues.