Stable knots and links in electromagnetic fields

TL;DR

This paper demonstrates that for any given link shape, there exists a null electromagnetic field configuration in free space where electric and magnetic field lines form that shape and remain topologically unchanged over time.

Contribution

It proves the existence of electromagnetic fields with prescribed stable topologies of field lines, showing topological invariance in null electromagnetic fields.

Findings

Existence of electromagnetic fields with arbitrary stable link topologies.

Electric and magnetic field lines remain topologically invariant over time.

Field lines can be shaped as any desired link in free space.

Abstract

In null electromagnetic fields the electric and the magnetic field lines evolve like unbreakable elastic filaments in a fluid flow. In particular, their topology is preserved for all time. We prove that for every link $L$ there is such an electromagnetic field that satisfies Maxwell's equations in free space and that has closed electric and magnetic field lines in the shape of $L$ for all time.