Chern-Simons modified gravity and closed time-like curves

TL;DR

This paper investigates G"odel-type solutions in four-dimensional Chern-Simons modified gravity, revealing the existence of vacuum solutions and hyperbolic causal solutions with matter, which differ from general relativity.

Contribution

It demonstrates the existence of vacuum solutions and hyperbolic causal solutions in Chern-Simons modified gravity, unlike in general relativity.

Findings

Vacuum solutions are possible in the theory.

Hyperbolic causal solutions exist with matter.

Differences from general relativity are established.

Abstract

We verify the consistency of the G\"odel-type solutions within the four-dimensional Chern-Simons modified gravity with the non-dynamical Chern-Simons coefficient, for different forms of matter including dust, fluid, scalar field and electromagnetic field, and the related causality issues. Unlike the general relativity, the vacuum solution turns out to be possible in our theory. Another essentially new result of our theory having no analogue in the general relativity consists in the existence of the hyperbolic causal solutions for the physically well-motivated matter.