  We derive a superpotential for null electromagnetic fields in which the field
line structure is in the form of an arbitrary torus knot. These fields are
shown to correspond to single copies of a class of anti-self-dual Kerr-Schild
spacetimes containing the Sparling-Tod metric. This metric is the pure Weyl
double copy of the electromagnetic Hopfion, and we show that the Eguchi-Hanson
metric is a mixed Weyl double copy of this Hopfion and its conformally inverted
state. We formulate two conditions for electromagnetic fields, generalizing
torus knotted fields and linked optical vortices, that, via the zero rest mass
equation for spin 1 and spin 2, defines solutions of linearized Einstein's
equation possessing a Hopf fibration as the curves along which no stretching,
compression or precession will occur. We report on numerical findings relating
the stability of the linked and knotted zeros of the Weyl tensor and their
relation to linked optical vortices.
