Weyl fermions in a family of G\"{o}del-type geometries with a topological defect

In this paper we study Weyl fermions in a family of G"odel-type geometries in Einstein general relativity. We also consider that these solutions are embedded in a topological defect background. We solve the Weyl equation and find the energy eigenvalues and eigenspinors for all three cases of G"odel-type geometries where a topological defect is passing through them. We show that the presence of a topological in these geometries contributes to modification of the spectrum of energy. The energy zero modes for all three cases of the G"odel geometries are discussed.