[Régions extérieures de l'espace-temps de Kerr perturbé par une non-linéarité vérifiant une décroissance de « peeling »]
On démontre, à l'extérieur de la région d'influence d'une boule de rayon centée à l'origine de l'hypersurface initiale , l'existence de solutions globales près de l'espace-temps de Kerr pourvu que les données initiales soient suffisamment proches de celles de Kerr. Cette région extérieure est la partie « éloignée » de la région extérieure de l'espace-temps de Kerr perturbée. De plus si on suppose que les corrections de la métrique de Kerr décroissent suffisamment vite, , on démontre que la décroissance vers zéro des composantes du tenseur de Riemann est en accord avec la « conjecture de peeling ».
We prove, outside the influence region of a ball of radius centered at the origin of the initial data hypersurface, , the existence of global solutions near to the Kerr spacetime, provided that the initial data are sufficiently near to those of Kerr. This external region is the “far” part of the outer region of the perturbed Kerr spacetime. Moreover, if we assume that the corrections to the Kerr metric decay sufficiently fast, , we prove that the various null components of the Riemann tensor decay in agreement with the “Peeling conjecture”.
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@article{CRMATH_2010__348_19-20_1123_0,
author = {Giulio Caciotta and Francesco Nicol\`o},
title = {External regions of nonlinearly perturbed {Kerr} spacetimes satisfying the peeling decay},
journal = {Comptes Rendus. Math\'ematique},
pages = {1123--1128},
publisher = {Elsevier},
volume = {348},
number = {19-20},
year = {2010},
doi = {10.1016/j.crma.2010.06.009},
language = {en},
}
TY - JOUR AU - Giulio Caciotta AU - Francesco Nicolò TI - External regions of nonlinearly perturbed Kerr spacetimes satisfying the peeling decay JO - Comptes Rendus. Mathématique PY - 2010 SP - 1123 EP - 1128 VL - 348 IS - 19-20 PB - Elsevier DO - 10.1016/j.crma.2010.06.009 LA - en ID - CRMATH_2010__348_19-20_1123_0 ER -
Giulio Caciotta; Francesco Nicolò. External regions of nonlinearly perturbed Kerr spacetimes satisfying the peeling decay. Comptes Rendus. Mathématique, Volume 348 (2010) no. 19-20, pp. 1123-1128. doi : 10.1016/j.crma.2010.06.009. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.06.009/
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