Knotted solutions, from electromagnetism to fluid dynamics

TL;DR

This paper explores knotted solutions in electromagnetism and fluid dynamics, revealing their connections and extending solutions to nonlinear theories and nonrelativistic fluids, with implications across physics.

Contribution

It establishes a novel mapping between electromagnetism and fluid dynamics, enabling the construction of knotted solutions in both fields, including nonlinear and quantum-corrected theories.

Findings

Knotted electromagnetic solutions also solve nonlinear theories like Born-Infeld.

Null electromagnetic configurations correspond to null pressureless fluids.

The approach yields solutions to nonrelativistic Euler equations.

Abstract

Knotted solutions to electromagnetism and fluid dynamics are investigated, based on relations we find between the two subjects. We can write fluid dynamics in electromagnetism language, but only on an initial surface, or for linear perturbations, and we use this map to find knotted fluid solutions, as well as new electromagnetic solutions. We find that knotted solutions of Maxwell electromagnetism are also solutions of more general nonlinear theories, like Born-Infeld, and including ones which contain quantum corrections from couplings with other modes, like Euler-Heisenberg and string theory DBI. Null configurations in electromagnetism can be described as a null pressureless fluid, and from this map we can find null fluid knotted solutions. A type of nonrelativistic reduction of the relativistic fluid equations is described, which allows us to find also solutions of the (nonrelativistic) Euler's equations.