The Non-Null and Force-Free Electromagnetic Field

TL;DR

This paper develops a covariant formalism linking non-null force-free electrodynamics solutions to spacetime foliations, deriving a general current density expression and exploring dual solutions in vacuum fields.

Contribution

It introduces a new covariant framework for non-null force-free electrodynamics and derives a general current density expression, expanding understanding of dual solutions.

Findings

Solutions can produce dual solutions only in vacuum fields

The formalism connects electrodynamics solutions with spacetime foliations

Illustrations include known solutions

Abstract

In this paper, we present a covariant formalism that connects solutions to force-free electrodynamics in the non-null case and foliations of spacetime. In doing so, we are also able to derive an expression of the general non-null current density vector. Just as in the null case, solutions in the non-null case can give rise to a dual solution, however, as is shown below, this can happen only when the solution describes a vacuum field. All theorems are illustrated with previously known solutions.