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We derive a superpotential for null electromagnetic fields in which the fieldline structure is in the form of an arbitrary torus knot. These fields areshown to correspond to single copies of a class of anti-self-dual Kerr-Schildspacetimes containing the Sparling-Tod metric. This metric is the pure Weyldouble copy of the electromagnetic Hopfion, and we show that the Eguchi-Hansonmetric is a mixed Weyl double copy of this Hopfion and its conformally invertedstate. We formulate two conditions for electromagnetic fields, generalizingtorus knotted fields and linked optical vortices, that, via the zero rest massequation for spin 1 and spin 2, defines solutions of linearized Einstein'sequation possessing a Hopf fibration as the curves along which no stretching,compression or precession will occur. We report on numerical findings relatingthe stability of the linked and knotted zeros of the Weyl tensor and theirrelation to linked optical vortices.

Anti-Self-Dual Spacetimes, Gravitational Instantons and Knotted Zeros of the Weyl Tensor