Gödel universe from string theory

The Gödel universe is a direct product of a line and a three-dimensional spacetime we call G$$_\alpha $$. In this paper, we show that the Gödel metrics can arise as exact solutions in Einstein–Maxwell–Axion, Einstein–Proca–Axion, or Freedman–Schwarz gauged supergravity theories. The last option allows us to embed the Gödel 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 Gödel black holes that are constructed from the double Wick rotations of the Gödel metrics