Cylindrical wormholes

TL;DR

This paper demonstrates that static, cylindrically symmetric wormholes can exist without violating energy conditions and with less exotic matter than spherical wormholes, providing explicit solutions with various fields.

Contribution

It shows the possibility of cylindrically symmetric wormholes without exotic matter and provides explicit solutions with scalar, spinor, and electromagnetic fields.

Findings

Cylindrical wormholes can exist without violating energy conditions.

Explicit solutions with scalar, spinor, and electromagnetic fields are constructed.

A no-go theorem states flat asymptotic behavior requires negative energy density.

Abstract

It is shown that the existence of static, cylindrically symmetric wormholes does not require violation of the weak or null energy conditions near the throat, and cylindrically symmetric wormhole geometries can appear with less exotic sources than wormholes whose throats have a spherical topology. Examples of exact wormhole solutions are given with scalar, spinor and electromagnetic fields as sources, and these fields are not necessarily phantom. In particular, there are wormhole solutions for a massless, minimally coupled scalar field in the presence of a negative cosmological constant, and for an azimuthal Maxwell electromagnetic field. All these solutions are not asymptotically flat. A no-go theorem is proved, according to which a flat (or string) asymptotic behavior on both sides of a cylindrical wormhole throat is impossible if the energy density of matter is everywhere nonnegative.