Chern-Simons modified gravity and closed timelike curves

Abstract

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