The Null and Force-Free Electromagnetic Field

TL;DR

This paper explores the geometric structure of null, force-free electromagnetic fields, detailing the spacetime foliations involved and illustrating the theory with an explicit FLRW spacetime example.

Contribution

It provides a coordinate-free geometric description of null, force-free electrodynamics and constructs explicit solutions in FLRW spacetime, extending previous work on spacetime foliations.

Findings

Characterization of null, force-free fields via spacetime foliations

Explicit construction of solutions in FLRW spacetime

General geometric framework for null force-free electrodynamics

Abstract

This paper describes the electrodynamics of a null and force-free field in completely geometric terms. As was previously established in \cite{Menon_FF20}, solutions to force-free electrodynamics are governed by the existence of certain special types of foliations of spacetime. Here the nature of the foliations in a coordinate-free formalism in the null case is prescribed. All of the general results are illustrated by constructing a null, force-free electrodynamic field in a Friedmann-Lemaitre-Robertson- Walker (FLRW) spacetime.