# On a remarkable electromagnetic field in the Einstein Universe

## TL;DR

This paper constructs a time-dependent electromagnetic field solution in the Einstein universe, demonstrating a knotted, finite energy, radiating configuration that can be translated into flat spacetime, with implications for cosmological models.

## Contribution

It introduces a novel, explicit electromagnetic solution in the Einstein universe and relates it to flat spacetime via conformal equivalence, expanding understanding of electromagnetic fields in curved and cosmological settings.

## Key findings

- Derived a knotted electromagnetic solution in Einstein universe
- Mapped the solution to flat spacetime using conformal equivalence
- Analyzed electromagnetic fields in expanding Friedmann models

## Abstract

We present a time-dependent solution of the Maxwell equations in the Einstein universe, whose electric and magnetic fields, as seen by the stationary observers, are aligned with the Clifford parallels of the $3$-sphere $S^3$. The conformal equivalence between Minkowski's spacetime and (a region of) the Einstein cylinder is then exploited in order to obtain a knotted, finite energy, radiating solution of the Maxwell equations in flat spacetime. We also discuss similar electromagnetic fields in expanding closed Friedmann models, and compute the matter content of such configurations.