Gödel universes in string theory

We show that homogeneous Gödel spacetimes need not contain closed timelike curves in low-energy-effective string theories. We find exact solutions for the Gödel metric in string theory for the full $O\left({\alpha }^{\prime }\right)$ action including both dilaton and axion fields. The results are valid for bosonic, heterotic and super-strings. To first order in the inverse string tension ${\alpha }^{\prime },$ these solutions display a simple relation between the angular velocity of the Gödel universe, Ω, and the inverse string tension of the form ${\alpha }^{\prime }=1/{\Omega }^2$ in the absence of the axion field. The generalization of this relationship is also found when the axion field is present.