TL;DR
This paper develops a method to transform cylindrical magnetovac solutions into toroidal configurations, providing an analytic Einstein-Maxwell solution for a toroidal magnetic field and matching it to an exterior spacetime.
Contribution
It introduces a novel mapping technique from cylindrical to toroidal magnetovac solutions and presents an explicit Einstein-Maxwell solution with boundary matching.
Findings
Successful mapping of cylinder to torus topology
Analytic solution for toroidal magnetic fields in Einstein-Maxwell theory
Matching of interior solution to asymptotically flat exterior
Abstract
A method for mapping known cylindrical magnetovac solutions to solutions in torus coordinates is developed. Identification of the cylinder ends changes topology from R1 x S1 to S1 x S1. An analytic Einstein-Maxwell solution for a toroidal magnetic field in tori is presented. The toroidal interior is matched to an asymptotically flat vacuum exterior, connected by an Israel boundary layer.
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