Rotating cylindrical wormholes: a no-go theorem

The existing solutions to the Einstein equations describing rotating cylindrical wormholes are not asymptotically flat and therefore cannot describe wormhole entrances as local objects in our Universe. To overcome this difficulty, flat asymptotic regions are added to wormhole solutions by matching them at some surfaces $\Sigma_-$ and $\Sigma_+$. It is shown, however, that if the wormhole solution is obtained for scalar fields with arbitrary potentials, possibly interacting with an azimuthal electric or magnetic field, then the matter content of one or both thin shells appearing on $\Sigma_-$ and $\Sigma_+$ violate the Null Energy Condition. Thus exotic matter is still necessary for obtaining a twice asymptotically flat wormhole.