Nontrivial Causal Structures Engendered by Knotted Solitons

Abstract

It is shown that the causal structure associated to string-like solutions of the Fadeev-Niemi (FN) model is described by an effective metric. Remarkably, the surfaces characterising the causal replacement depend on the energy momentum tensor of the background soliton and carry implicitly a topological invariant ${\pi }_3({\mathbb{S}}^2)$. As a consequence, it follows that the pre- image curves in ${\mathbb{R}}^3$ nontrivialy define directions where the cones remain unchanged. It turns out that these results may be of importance in understanding time dependent solutions (collisions/scatterings) numerically or analytically.

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Cited by in corpus (2)

• Characteristic analysis for integrable soliton models on two-dimensional target spaces
• From Hopf fibrations to exotic causal replacements