Partial Differential Equations/Mathematical Physics
Global solutions, and their decay properties, of the spherically symmetric su(2) — Einstein–Yang–Mills–Higgs equations
Comptes Rendus. Mathématique, Volume 349 (2011) no. 19-20, pp. 1067-1072.

We generalize, to the su(2) — Einstein–Yang–Mills–Higgs system, previous results concerning global solutions of the Einstein-scalar field and the Einstein–Maxwell–Higgs equations. The novelty of the present work is at least twofold. For one thing the assumption on the self-interaction potential is improved. For another thing explanation is furnished why the solutions obtained here decay slower than those of self-gravitating massless scalar fields. Actually this latter phenomenon stems from the non-vanishing of the local charge.

Nous généralisons, aux équations dʼEinstein–Yang–Mills–Higgs, des résultats antérieurs concernant les systèmes Einstein-champ scalaire et Einstein–Maxwell–Higgs. Lʼoriginalité de notre travail est au moins double. Premièrement lʼhypothèse sur le potentiel dʼinteraction est améliorée. Deuxièmement une explication est donnée du fait que les solutions établies ici décroissent moins vite que celles obtenues dans le cas des équations dʼEinstein-champ scalaire. En effet ce dernier phénomène est dû à la non-nullité de la charge locale.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2011.09.004
Tadmon, Calvin 1

1 Department of Mathematics and Computer Science, Faculty of Science, University of Dschang, PO Box 67, Dschang, Cameroon
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Tadmon, Calvin. Global solutions, and their decay properties, of the spherically symmetric $ \mathfrak{su}(2)$ — Einstein–Yang–Mills–Higgs equations. Comptes Rendus. Mathématique, Volume 349 (2011) no. 19-20, pp. 1067-1072. doi : 10.1016/j.crma.2011.09.004. http://www.numdam.org/articles/10.1016/j.crma.2011.09.004/

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