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Comptes Rendus Mathématique
Volume 349, n° 19-20
pages 1067-1072 (novembre 2011)
Doi : 10.1016/j.crma.2011.09.004
Received : 21 May 2011 ;  accepted : 7 September 2011
Global solutions, and their decay properties, of the spherically symmetric   — Einstein–Yang–Mills–Higgs equations
Solutions globales et estimations de décroissance pour les équations dʼEinstein–Yang–Mills–Higgs en symétrie sphérique
 

Calvin Tadmon
Department of Mathematics and Computer Science, Faculty of Science, University of Dschang, PO Box 67, Dschang, Cameroon 

Abstract

We generalize, to the   — 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.

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Résumé

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.

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