Stationary Solutions in 2+1 Dimensional Gravity and Closed Time-Like Curves

TL;DR

This paper derives general solutions for 2+1 dimensional gravity in a radial gauge and demonstrates that under certain conditions, closed time-like curves cannot occur at spatial infinity.

Contribution

It provides a complete solution for stationary 2+1D gravity metrics and proves the non-existence of CTCs at infinity under specific energy and boundary conditions.

Findings

General solutions expressed in quadratures using reduced radial gauge

Proof that weak energy condition and no CTC at infinity prevent CTCs

Applicable to conical universes at infinity

Abstract

We apply the reduced radial gauge to give the general solution of the metric in 2+1 dimensions in term of quadratures. It allows a complete controll on the support of the source. We use the result to prove that for a general stationary universe, conical at infinity, the weak energy condition and the absence of CTC at space infinity prevent the occurrrence of any CTC.