This paper contains a discussion of a relativistic spin-0 system in the presence of a Gödel-type background space-time. The Duffin-Kemmer-Petiau (DKP) equation in the presence of a Gödel-type background space-time is studied in detail. After a derivation of the final form of this equation in the considered framework, free spin-0 particles have been studied.

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In this paper, the Gödel-type space-times have been considered. We are interested in the investigation of relativistic free bosons in the Gödel-type space-times. Therefore, the Klein–Gordon equation considering the Gödel-type space-times has been constructed in a general manner. Then to accomplish our goal, two well-known special cases have been considered for the unknown function in the tensor metric of the Gödel-type space-times. The explicit forms of the wave functions for each case as well as the energy eigenvalue equations have been derived in detail.

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