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There are no Magnetically Charged Particle-like Solutions of the Einstein Yang-Mills Equations for Models with an Abelian Residual Group

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Abstract

We prove that there are no magnetically charged particle-like solutions for any model with an Abelian residual group in Einstein Yang-Mills, but for the non-Abelian models the possibility remains open. An analysis of the Lie algebraic structure of the Yang-Mills fields is essential to our results. In one key step of our analysis we use invariant polynomials to determine which orbits of the gauge group contain the possible asymptotic Yang-Mills field configurations. Together with a new horizontal/vertical space decomposition of the Yang-Mills fields this enables us to overcome some obstacles and complete a dynamical system existence theorem for asymptotic solutions with nonzero total magnetic charge. We then prove that these solutions cannot be extended globally for Abelian models and begin an investigation of the details for non-Abelian models.

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Authors and Affiliations

  1. School of Mathematical Sciences, Monash University, Melbourne, VIC, 3800, Australia

    Mark Fisher & Todd A. Oliynyk

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  1. Mark Fisher
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  2. Todd A. Oliynyk
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Correspondence to Mark Fisher.

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Communicated by P. T. Chruściel

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Fisher, M., Oliynyk, T.A. There are no Magnetically Charged Particle-like Solutions of the Einstein Yang-Mills Equations for Models with an Abelian Residual Group. Commun. Math. Phys. 312, 137–177 (2012). https://doi.org/10.1007/s00220-011-1388-5

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  • DOI: https://doi.org/10.1007/s00220-011-1388-5

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