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Title: On spacetime foliations and electromagnetic knots.
Authors: Silva, Wanderson Costa e
Costa, Érico Goulart de Oliveira
Ottoni, José Eloy
Keywords: Topological solutions
Spacetime foliations
Hopf fiberings
Field lines
Issue Date: 2022
Citation: SILVA, W. C. e.; COSTA, E. G. de O.; OTTONI, J. E. On spacetime foliations and electromagnetic knots. Journal of Physics A-Mathematical and Theoretical, v. 52, n. 26, artigo 265203, 2019. Disponível em: <>. Acesso em: 06 jul. 2022.
Abstract: The present paper has a number of distinct purposes. First is to give a description of a class of electromagnetic knots from the perspective of foliation theory. Knotted solutions are then interpreted in terms of two codimension-2 foliations whose knotted leaves intersect orthogonally everywhere in spacetime. Secondly, we show how the foliations give rise to field lines and how the topological invariants emerge. The machinery used here emphasizes intrinsic properties of the leaves instead of observer dependent quantities—such as a time function, a local rest frame or a Cauchy hypersurface. Finally, we discuss the celebrated Hopf–Rañada solution in details and stress how the foliation approach may help in future developments of the theory of electromagnetic knots. We conclude with several possible applications, extensions and generalizations.
ISSN: 1751-8121
Appears in Collections:DEMAT - Artigos publicados em periódicos

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