Rotating cylindrical wormholes: a no-go theorem

TL;DR

This paper proves a no-go theorem showing that rotating cylindrical wormholes cannot be made asymptotically flat without exotic matter, even with scalar fields and electromagnetic interactions, thus confirming the necessity of exotic matter.

Contribution

It demonstrates that matching non-asymptotically flat rotating cylindrical wormholes to flat regions inevitably requires matter violating energy conditions, extending previous no-go results.

Findings

Asymptotically flat rotating cylindrical wormholes require exotic matter.

Matching solutions with scalar fields and electromagnetic fields still violates energy conditions.

Exotic matter remains necessary for physically realistic wormhole models.

Abstract

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.