Exotic spacetimes, superconducting strings with linear momentum, and (not quite) all that

TL;DR

This paper derives and analyzes exact vacuum solutions for cylindrically symmetric spacetimes, revealing exotic properties like closed causal curves, and discusses their potential physical sources, especially in relation to superconducting strings with currents and momentum.

Contribution

It provides a comprehensive derivation of stationary, non-rotating cylindrically symmetric vacuum metrics and explores their exotic features and physical plausibility, contrasting previous models.

Findings

Some exotic metrics admit closed causal curves and geodesic trapping.

Physical sources for these metrics must violate the dominant energy condition under certain restrictions.

External vacuum metrics are non-exotic if matter in shells satisfies the DEC.

Abstract

We derive the general exact vacuum metrics associated with a stationary (non static), non rotating, cylindrically symmetric source. An analysis of the geometry described by these vacuum metrics shows that they contain a subfamily of metrics that, although admitting a consistent time orientation, display "exotic" properties, such as "trapping" of geodesics and closed causal curves through every point. The possibility that such spacetimes could be generated by a superconducting string, endowed with a neutral current and momentum, has recently been considered by Thatcher and Morgan. Our results, however, differ from those found by Thatcher and Morgan, and the discrepancy is explained. We also analyze the general possibility of constructing physical sources for the exotic metrics, and find that, under certain restrictions, they must always violate the dominant energy condition (DEC). We illustrate our results by explicitly analyzing the case of concentric shells, where we find that in all cases the external vacuum metric is non exotic if the matter in the shells satisfies the DEC.