  Any interior solution for a cylindrically symmetric, stationary cosmic string
with flat exterior, spinning around its longitudinal axis, and without internal
longitudinal currents ($g_{zz}=1$, $g_{tz}=0$), must somewhere violate the weak
energy condition of standard general relativity. Existing interior solutions
may be readily fixed by adding mass to the string above that generating its
angular deficit, but at the cost of introducing an exterior gravitational
field.
