Cosmological electromagnetic Hopfions

Sergio A. Hojman, Felipe A. Asenjo

Research output: Contribution to journalArticlepeer-review


It is shown that any mathematical solution for null electromagnetic field knots in flat spacetime is also a null field knotted solution for cosmological electromagnetic fields. This is obtained by replacing the time t → τ = ∫dt/a, where a = a(t) is the scale factor of the Universe described by the Friedman-Lemaître-Robertson-Walker (FLRW) cosmology, and by adequately rewriting the (empty flat spacetimes) electromagnetic fields solutions in a medium defined by the FLRW metric. We found that the dispersion (evolution) of electromagnetic Hopfions is faster on cosmological scenarios. We discuss the implications of these results for different cosmological models.

Original languageEnglish
Article number055514
JournalPhysica Scripta
Issue number5
StatePublished - 1 May 2024
Externally publishedYes


  • Hopfions
  • cosmology
  • electromagnetism


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