Bounded, asymptotically flat toroidal exteriors for cylindrically symmetric spacetimes

TL;DR

This paper presents a model for smoothly matching a charged, massive toroidal exterior to a cylindrical interior in general relativity, using electric fields to satisfy energy conditions and create bounded cosmic string-like structures.

Contribution

It introduces a novel transitional layer that compensates for geometric changes via electric fields, enabling bounded, asymptotically flat toroidal exteriors in cylindrically symmetric spacetimes.

Findings

Successful matching of exterior and interior geometries.

Electric field gradients compensate for energy condition violations.

Example of creating a bounded cosmic string with an angular deficit.

Abstract

A transitional layer matching the asymptotically flat exterior of a charged, massive toroidal body to an interior with spatially cylindrical symmetry is described. The changes in the geometry, which by themselves would require an energy tensor violating the energy conditions of classical general relativity, are compensated for by an additional strong electric field. Part of its gradient is consumed, depending on how much the exterior toroid departs from local cylindrical symmetry; what is left over can be used to effect further transitions in the cylindrical interior. An example is given of such a transition creating an angular deficit, allowing an otherwise infinite cosmic string to be captured within a bounded source.