Arrayás, ManuelFernández-Rañada, AntonioTiemblo, AlfredoTrueba, José Luis2025-01-092025-01-092019-09-02Arrayás, M.; Rañada, A.F.; Tiemblo, A.; Trueba, J.L. Null Electromagnetic Fields from Dilatation and Rotation Transformations of the Hopfion. Symmetry 2019, 11, 1105. https://doi.org/10.3390/sym110911052073-8994https://hdl.handle.net/10115/53097The application of topology concepts to Maxwell equations has led to the developing of the whole area of electromagnetic knots. In this paper, we apply some symmetry transformations to a particular electromagnetic knot, the hopfion field, to get a new set of knotted solutions with the properties of being null. The new fields are obtained by a homothetic transformation (dilatation) and a rotation of the hopfion, and we study the constraints that the transformations must fulfill in order to generate valid electromagnetic fields propagating in a vacuum. We make use of the Bateman construction and calculate the four-potentials and the electromagnetic helicities. It is observed that the topology of the field lines does not seem to be conserved as it is for the hopfion.enAttribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/HopfionBateman ConstructionNull FieldsArticlehttps://doi.org/10.3390/sym11091105info:eu-repo/semantics/openAccess