JOURNAL OF COSMOLOGY AND ASTROPARTICLE PHYSICS, cilt.2014, sa.7, 2014 (SCI-Expanded)
In this paper, we study Noether gauge symmetries of geodesic motion for geodesic Lagrangian of four classes of metrics of Godel-type spacetimes for which we calculated the Noet her gauge symmetries for all classes I-IV, and find the first integrals of corresponding classes to derive a complete characterization of the geodesic motion. Using the obtained expressions for <(t)over dot>, <(r)over dot>, <(phi)over dot> and <(z)over dot> of each classes I-IV which depends essentially on two independent parameters 711 and to, we explicitly integrated the geodesic equations of motion for the corresponding Godel-type space times.