Nonlinear electrodynamics is skilled with knots

Centro Brasileiro de Pesquisas Físicas - CBPF, Rua Dr. Xavier Sigaud, 150, CEP 22290-180, Rio de Janeiro, Brazil

Received: 7 April 2016
Accepted: 11 July 2016

Abstract

The aim of this letter is threefold: First is to show that nonlinear generalizations of electrodynamics support various types of knotted solutions in vacuum. The solutions are universal in the sense that they do not depend on the specific Lagrangian density, at least if the latter gives rise to a well-posed theory. Second, is to describe the interaction between probe waves and knotted background configurations. We show that the qualitative behaviour of this interaction may be described in terms of Robinson congruences, which appear explicitly in the causal structure of the theory. Finally, we argue that optical arrangements endowed with intense background fields could be the natural place to look for the knots experimentally.