[Solutions globales et estimations de décroissance pour les équations dʼEinstein–Yang–Mills–Higgs en symétrie sphérique]
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.
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.
Accepté le :
Publié le :
@article{CRMATH_2011__349_19-20_1067_0,
author = {Tadmon, Calvin},
title = {Global solutions, and their decay properties, of the spherically symmetric $ \mathfrak{su}(2)$ {\textemdash} {Einstein{\textendash}Yang{\textendash}Mills{\textendash}Higgs} equations},
journal = {Comptes Rendus. Math\'ematique},
pages = {1067--1072},
publisher = {Elsevier},
volume = {349},
number = {19-20},
year = {2011},
doi = {10.1016/j.crma.2011.09.004},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2011.09.004/}
}
TY - JOUR
AU - Tadmon, Calvin
TI - Global solutions, and their decay properties, of the spherically symmetric $ \mathfrak{su}(2)$ — Einstein–Yang–Mills–Higgs equations
JO - Comptes Rendus. Mathématique
PY - 2011
SP - 1067
EP - 1072
VL - 349
IS - 19-20
PB - Elsevier
UR - http://www.numdam.org/articles/10.1016/j.crma.2011.09.004/
DO - 10.1016/j.crma.2011.09.004
LA - en
ID - CRMATH_2011__349_19-20_1067_0
ER -
%0 Journal Article
%A Tadmon, Calvin
%T Global solutions, and their decay properties, of the spherically symmetric $ \mathfrak{su}(2)$ — Einstein–Yang–Mills–Higgs equations
%J Comptes Rendus. Mathématique
%D 2011
%P 1067-1072
%V 349
%N 19-20
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2011.09.004/
%R 10.1016/j.crma.2011.09.004
%G en
%F CRMATH_2011__349_19-20_1067_0
Tadmon, Calvin. Global solutions, and their decay properties, of the spherically symmetric $ \mathfrak{su}(2)$ — Einstein–Yang–Mills–Higgs equations. Comptes Rendus. Mathématique, Tome 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/
[1] Global existence of spherically symmetric solutions to the coupled Einstein and nonlinear Klein–Gordon system, Classical Quantum Gravity, Volume 18 (2001) no. 21, pp. 4589-4605
[2] Global existence of solutions to the coupled Einstein and Maxwell–Higgs system in the spherical symmetry, Ann. Henri Poincaré, Volume 4 (2003), pp. 35-62
[3] Yang–Mills–Higgs fields in three space time dimensions, Mém. Soc. Math. France, Volume 46 (1991), pp. 73-97
[4] The problem of a self-gravitating scalar field, Comm. Math. Phys., Volume 105 (1986), pp. 337-361
[5] The Goursat problem for the Einstein–Yang–Mills–Higgs system in weighted Sobolev spaces, C. R. Acad. Sci. Paris, Ser. I, Volume 348 (2010), pp. 35-39
[6] The characteristic initial value problem for the Einstein–Yang–Mills–Higgs system in weighted Sobolev spaces, Appl. Math. Res. Express, Volume 2010 (2010) no. 2, pp. 154-231
[7] Conformal treatment of infinity, Relativ. Groups Topology, Volume 43 (1964), pp. 565-584 (republished in Gen. Relativity Gravitation, 2011, pp. 901-922)
Cité par Sources :
