Linked and knotted structures in physics (Jan Willem Dalhuisen)

janwillem-knots Figure: A recently (re)discovered topological non trivial solution to Maxwell equations in vacuum, known as a knot of light, in which any two electric (magnetic) fi eld lines are linked once, in such a way that they collectively form a Hopf-fibration.

 

1. electrodynamics

We theoretically investigate properties of knots of light, such as their behavior when el- ements of the symmetry group act on them. With the help of advanced mathematical theories and in collaboration with the department of mathematics, we investigate general- isations of the known linked solutions of Maxwell equations. Part of the results will be of importance for the study of knotted structures in plasma physics, also a research subject in the QMO group.

2. general relativity

Like knots of light in Maxwell theory, linked and knotted solutions to the linearised Einstein equations have also been found ("knots of gravity", gravitational waves). We investigate the possibilities of knotted structures in the full (non-linear) Einstein equations. We consider vacuum and also sourced solutions.