Godel Universe from String Theory

TL;DR

This paper demonstrates how G"odel universe solutions can be embedded in string theory through specific supergravity models, revealing connections to black holes and higher-dimensional geometries.

Contribution

It shows that G"odel metrics are exact solutions in various supergravity theories and embeds them into string theory via a specific ten-dimensional construction.

Findings

G"odel metrics arise as solutions in Einstein-Maxwell-Axion, Einstein-Proca-Axion, and gauged supergravity.

The ten-dimensional embedding relates to D1/D5/D5 brane intersections.

G"odel black holes are constructed from metric double Wick rotations.

Abstract

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.