Rotating cylindrical wormholes

Abstract

We consider stationary, cylindrically symmetric configurations in general relativity and formulate necessary conditions for the existence of rotating cylindrical wormholes. It is shown that in a comoving reference frame the rotational part of the gravitational field is separated from its static part and forms an effective stress-energy tensor with exotic properties, which favors the existence of wormhole throats. Exact vacuum and scalar-vacuum solutions (with a massless scalar) are considered as examples, and it turns out that even vacuum solutions can be of wormhole nature. However, solutions obtainable in this manner cannot have well-behaved asymptotic regions, which excludes the existence of wormhole entrances appearing as local objects in our Universe. To overcome this difficulty, we try to build configurations with flat asymptotic regions by the cut-and-paste procedure: on both sides of the throat, a wormhole solution is matched to a properly chosen region of flat space at some surfaces $Σ_-$ and $Σ_+$. It is shown, however, that if we describe the throat region with vacuum or scalar-vacuum solutions, one or both thin shells appearing on $Σ_-$ and $Σ_+$ inevitably violate the null energy condition. In other words, although rotating wormhole solutions are easily found without exotic matter, such matter is still necessary for obtaining asymptotic flatness.