Joe Swearngin, Amy Thompson, Alexander Wickes, Jan Willem Dalhuisen, Dirk Bouwmeester
Linked field configurations, in particular those related to the Hopf fibration, have been considered in many branches of physics such as electromagnetism [1, 2, 3], magnetohydrodynamics [4], hadronic physics [5, 6], helium superfluids [7], and Bose-Einstein condensates [8]. In the case of the electromagnetic knot (EM knot), the salient feature of the Hopf structure is defined by the Poynting vector which is tangent to a Hopf fibration that propagates at the speed of light without deformation. This Poynting vector structure forms a Robinson congruence which plays a central role in twistor theory [9, 10]. Here we first show that the EM knot represents the simplest nontrivial solution to the spin-1 massless field equation in twistor space. Next, we extend the solution to the spin-N equations. We conclude by analyzing the spin-2 solution within the framework of gravito-electromagnetism [11, 12]. By decomposing the spin-2 field into the spatial gravito-electric and gravito-magnetic tensors we characterize their topological structure in terms of the EM knot.
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http://arxiv.org/abs/1302.1431
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