Chern-Simons modified gravity and closed time-like curves

Understand

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.