2+1 Gravity and Closed Time-Like Curves

TL;DR

This paper applies the radial gauge to 2+1 dimensional gravity, deriving explicit solutions and conditions under which closed time-like curves are absent, with implications for cosmological models.

Contribution

It introduces a method using the radial gauge to solve 2+1 gravity problems explicitly and analyzes conditions preventing closed time-like curves.

Findings

Weak energy condition and asymptotic flatness imply no closed time-like curves at infinity.

Explicit formulas for stationary solutions in 2+1 gravity.

Potential application to cosmological solutions in lower dimensions.

Abstract

In this paper we report some results obtained by applying the radial gauge to 2+1 dimensional gravity. The general features of this gauge are reviewed and it is shown how they allow the general solution of the problem in terms of simple quadratures. Then we concentrate on the general stationary problem providing the explicit solving formulas for the metric and the explicit support conditions for the energy momentum tensor. The chosen gauge allows, due to its physical nature, to exploit the weak energy condition and in this connection it is proved that for an open universe conical at space infinity the weak energy condition and the absence of closed time like curves (CTC) at space infinity imply the total absence of CTC. It is pointed out how the approach can be used to examine cosmological solution in 2+1 dimensions.