  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.
