Godel Universes in String Theory

TL;DR

This paper demonstrates that G"odel universes can exist in string theory without closed timelike curves, providing exact solutions that relate the universe's rotation to string tension, applicable across various string theories.

Contribution

It presents the first exact solutions of G"odel spacetimes in string theory including dilaton and axion fields, establishing a relation between angular velocity and string tension.

Findings

G"odel solutions without closed timelike curves in string theory.

Exact solutions including dilaton and axion fields.

Relation between angular velocity and inverse string tension.

Abstract

We show that homogeneous G\"odel spacetimes need not contain closed timelike curves in low-energy-effective string theories. We find exact solutions for the G\"odel metric in string theory for the full $O(\alpha ^{\prime})$ 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 G\"odel universe, $\Omega ,$ 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.