Rotating Melvin-like universes and wormholes in general relativity

TL;DR

This paper presents exact solutions in general relativity describing rotating, cylindrically symmetric spacetimes with magnetic fields, including novel wormhole models that satisfy energy conditions and connect flat regions.

Contribution

It introduces new rotating cylindrical solutions with magnetic fields, including traversable wormholes that satisfy the Weak Energy Condition, expanding the class of physically plausible wormhole models.

Findings

Some solutions resemble Melvin's magnetic universe with a symmetry axis.

Certain solutions describe traversable wormholes without a symmetry axis.

The wormholes can be matched to flat space regions, satisfying energy conditions.

Abstract

We find a family of exact solutions to the Einstein-Maxwell equations for rotating cylindrically symmetric distributions of a perfect fluid with the equation of state $p = w\rho$ ($|w| < 1$), carrying a circular electric current in the angular direction. This current creates a magnetic field along the $z$ axis. Some of the solutions describe geometries resembling that of Melvin's static magnetic universe and contain a regular symmetry axis, while some others (in the case $w > 0$) describe traversable wormhole geometries which do not contain a symmetry axis. Unlike Melvin's solution, those with rotation and a magnetic field cannot be vacuum and require a current. The wormhole solutions admit matching with flat-space regions on both sides of the throat, thus forming a cylindrical wormhole configuration potentially visible for distant observers residing in flat or weakly curved parts of space. The thin shells, located at junctions between the inner (wormhole) and outer (flat) regions, consist of matter satisfying the Weak Energy Condition under a proper choice of the free parameters of the model, and thus we obtain new examples of phantom-free wormhole models in general relativity. In the limit $w \to 1$, the magnetic field tends to zero, and the wormhole model tends to the one obtained previously, where the source of gravity is stiff matter with the equation of state $p = \rho$.