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In this contribution, some solutions of the Klein-Gordon equation in theG\"odel-type metrics with an embedded cosmic string are considered. The quantumdynamics of a scalar particle in three spaces whose metric is described bydifferent classes of G\"odel solution, with a cosmic string passing through thespaces, is found. The energy levels and eigenfunctions of the Klein-Gordonoperator are obtained. We show that these eigenvalues and eigenfunctions dependon the parameter characterizing the presence of a cosmic string in thespace-time. We note that the presence of topological defects breaks thedegeneracy of energy levels.

Quantum Influence of Topological Defects in G\"odel-type Space-times