How much energy do closed timelike curves in 2+1 spacetimes need?

TL;DR

This paper demonstrates that in open 2+1 gravity, closed timelike curves are incompatible with timelike total energy momentum, suggesting energy conditions prevent their formation.

Contribution

It provides a simple argument linking energy conditions to the non-existence of closed timelike curves in 2+1 gravity.

Findings

Closed timelike curves cannot exist with timelike total energy momentum.

Polarized surfaces do not converge in the presence of timelike energy.

Energy conditions restrict the formation of closed timelike curves.

Abstract

By noticing that, in open 2+1 gravity, polarized surfaces cannot converge in the presence of timelike total energy momentum (except for a rotation of 2 pi), we give a simple argument which shows that, quite generally, closed timelike curves cannot exist in the presence of such energy condition.