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

Reinaldo J. Gleiser; Manuel H. Tiglio

doi:10.1103/PhysRevD.61.104006

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

Reinaldo J. Gleiser, Manuel H. Tiglio

DOI 10.1103/PhysRevD.61.104006 · Physical Review D

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Abstract

We derive the general exact vacuum metrics associated with a stationary (nonstatic), nonrotating, 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, displays “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 nonexotic if the matter in the shells satisfies the DEC.