The G\"{o}del solution in the modified gravity

TL;DR

This paper demonstrates that the G"{o}del metric, which admits closed timelike curves, remains a solution in a modified gravity theory combining Einstein-Hilbert and gravitational Chern-Simons terms, indicating such features are preserved.

Contribution

It shows that the G"{o}del solution persists in Chern-Simons modified gravity, extending the understanding of solutions in alternative gravity theories.

Findings

G"{o}del metric solves the modified equations of motion

Closed timelike curves are not forbidden in Chern-Simons gravity

The solution confirms the persistence of G"{o}del features in modified gravity

Abstract

We consider the modified gravity whose action represents itself as a sum of the usual Einstein-Hilbert action and the gravitational Chern-Simons term and show that the G\"{o}del metric solves the modified equations of motion, thus proving that the closed timelike curves whose presence is characteristic for the G\"{o}del solution are not forbidden in the case of the Chern-Simons modified gravity as well.