Inspecting Baby Skyrmions with Effective Metrics

Abstract

In the present paper we investigate the causal structure of the baby Skyrme model using appropriate geometrical tools. We discuss several features of excitations propagating on top of background solutions and show that the evolution of high frequency waves is governed by a curved effective geometry. Examples are given for which the effective metric describes the interaction between waves and solitonic solutions such as kinks, antikinks and Hedgehogs. In particular, it is shown how violent processes involving the collisions of solitons and antisolitons may induce metrics which are not globaly hyperbolic. We argue that it might be illuminating to calculate the effective metric as a diagnostic test for pathological regimes in numerical simulations.

arXiv comment15 pages, 5 figures

References in corpus (14)

• Low energy hadron physics in holographic QCD
• Analogue Gravity
• Geometrical aspects of light propagation in nonlinear electrodynamics
• Multisolitons in a Two-dimensional Skyrme Model
• Dynamics of Baby Skyrmions
• Light propagation in non-trivial QED vacua
• The baby Skyrme models and their multi-skyrmions
• Extended Supersymmetry and BPS solutions in baby Skyrme models
• Broken Baby Skyrmions
• Local and global well-posedness of wave maps on ${\mathbb{R}}^{1+1}$ for rough data
• On the hyperbolicity of Maxwell's equations with a local constitutive law
• Regular hyperbolicity, dominant energy condition and causality for Lagrangian theory of maps
• Causality and the Skyrme Model
• Skyrmion-anti-Skyrmion Annihilation with Omega Mesons

Cited by in corpus (2)

• Nontrivial Causal Structures Engendered by Knotted Solitons
• Characteristic analysis for integrable soliton models on two-dimensional target spaces