Rotating cylindrical wormholes and energy conditions

Abstract

We seek wormholes among rotating cylindrically symmetric configurations in general relativity. Exact wormhole solutions are presented with such sources of gravity as a massless scalar field, a cosmological constant, and a scalar field with an exponential potential. However, none of these solutions are asymptotically flat, which excludes the existence of wormhole entrances as local objects in our Universe. To overcome this difficulty, we try to build configurations with flat asymptotic regions using the cut-and-paste procedure: on both sides of the throat, a wormhole solution is matched to a properly chosen region of flat space-time at some surfaces $\Sigma_-$ and $\Sigma_+$. It is shown, however, that if the source of gravity in the throat region is a scalar field with an arbitrary potential, then one or both thin shells appearing on $\Sigma_-$ and $\Sigma_+$ inevitably violate the null energy condition. Thus, although rotating wormhole solutions are easily found without exotic matter, such matter is still necessary for obtaining asymptotic flatness.