Linked and Knotted Gravitational Radiation

Abstract

We show that the torus knot topology is inherent in electromagnetic and gravitational radiation by constructing spin-$N$ fields based on this topology from the elementary states of twistor theory. The twistor functions corresponding to the elementary states admit a parameterization in terms of the poloidal and toroidal winding numbers of the torus knots, allowing one to choose the degree of linking or knotting of the associated field configuration. Using the gravito-electromagnetic formalism, we show that the torus knot structure is exhibited in the tendex and vortex lines for the analogous linearized gravitational solutions. We describe the topology of the gravitational fields and its physical interpretation in terms of the tidal and frame drag forces of the gravitational field.