Potentially observable cylindrical wormholes without exotic matter in general relativity

Abstract

All known solutions to the Einstein equations describing rotating cylindrical wormholes lack asymptotic flatness and therefore cannot describe wormhole entrances as local objects in our Universe. To overcome this difficulty, wormhole solutions are joined to flat asymptotic regions at some surfaces $\Sigma_-$ and $\Sigma_+$. The whole configuration thus consists of three regions, the internal one containing a wormhole throat, and two flat external ones, considered in rotating reference frames. Using a special kind of anisotropic fluid respecting the Weak Energy Condition (WEC) as a source of gravity in the internal region, we show that the parameters of this configuration can be chosen in such a way that matter on both junction surfaces $\Sigma_-$ and $\Sigma_+$ also respects the WEC. Closed timelike curves are shown to be absent by construction in the whole configuration. It seems to be the first example of regular twice asymptotically flat wormholes without exotic matter and without closed timelike curves, obtained in general relativity.