Closed time like curve and the energy condition in 2+1 dimensional gravity

TL;DR

This paper proves that in 2+1 dimensional gravity with stationary, rotational sources, the weak energy condition and absence of CTC at infinity imply no closed timelike curves exist anywhere.

Contribution

It provides a direct proof linking energy conditions and the global causal structure in 2+1 dimensional gravity models.

Findings

No closed timelike curves if energy condition holds and universe is open

Absence of CTC at infinity implies absence everywhere under given conditions

Energy conditions constrain causal structure in lower-dimensional gravity

Abstract

We consider gravity in 2+1 dimensions in presence of extended stationary sources with rotational symmetry. We prove by direct use of Einstein's equations that if i) the energy momentum tensor satisfies the weak energy condition, ii) the universe is open (conical at space infinity), iii) there are no CTC at space infinity, then there are no CTC at all.