Godel Universe from String Theory

G"odel universe is a direct product of a line and a three-dimensional spacetime we call G${}_{\alpha }$. In this paper, we show that the G"odel metrics can arise as exact solutions in Einstein-Maxwell-Axion, Einstein-Proca-Axion, or Freedman-Schwarz gauged supergravity theories. The last allows us to embed G"odel universe in string theory. The ten-dimensional spacetime is a direct product of a line and the nine-dimensional one of an $S^3\times S^3$ bundle over G${}_{\alpha }$, and it can be interpreted as some decoupling limit of the rotating D1/D5/D5 intersection. For some appropriate parameter choice, the nine-dimensional metric becomes an AdS${}_3\times S^3$ bundle over squashed 3-sphere. We also study the properties of the G"odel black holes that are constructed from the double Wick rotations of the G"odel metrics.