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

TL;DR

This paper provides a comprehensive solution for stationary 2+1 dimensional gravity with extended sources and angular momentum, analyzing conditions for the existence of closed time-like curves and their relation to energy conditions.

Contribution

It offers the general explicit solution for stationary 2+1D gravity with sources and studies the conditions preventing closed time-like curves.

Findings

Closed time-like curves are prevented under weak energy conditions and absence at infinity.

Explicit solutions for stationary 2+1D gravity with angular momentum are derived.

The compact support property of the energy-momentum tensor is characterized.

Abstract

We give the general solution of the stationary problem of 2+1 dimensional gravity in presence of extended sources, also endowed with angular momentum. We solve explicitly the compact support property of the energy momentum tensor and we apply the results to the study of closed time-like curves. In the case of rotational symmetry we prove that the weak energy condition combined with the absence of closed time-like curves at space infinity prevents the existence of closed time-like curves everywhere in an open universe (conical space at infinity).