[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 = {Caciotta, Giulio and Nicol\`o, Francesco},
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},
url = {http://archive.numdam.org/articles/10.1016/j.crma.2010.06.009/}
}
TY - JOUR AU - Caciotta, Giulio AU - Nicolò, Francesco 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 UR - http://archive.numdam.org/articles/10.1016/j.crma.2010.06.009/ DO - 10.1016/j.crma.2010.06.009 LA - en ID - CRMATH_2010__348_19-20_1123_0 ER -
%0 Journal Article %A Caciotta, Giulio %A Nicolò, Francesco %T External regions of nonlinearly perturbed Kerr spacetimes satisfying the peeling decay %J Comptes Rendus. Mathématique %D 2010 %P 1123-1128 %V 348 %N 19-20 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2010.06.009/ %R 10.1016/j.crma.2010.06.009 %G en %F CRMATH_2010__348_19-20_1123_0
Caciotta, Giulio; Nicolò, Francesco. External regions of nonlinearly perturbed Kerr spacetimes satisfying the peeling decay. Comptes Rendus. Mathématique, Tome 348 (2010) no. 19-20, pp. 1123-1128. doi : 10.1016/j.crma.2010.06.009. http://archive.numdam.org/articles/10.1016/j.crma.2010.06.009/
[1] Decay of the Maxwell field on the Schwarzschild manifold, Journal of Hyperbolic Differential Equations, Volume 5 (2008) no. 4, pp. 807-856
[2] The nonlinear perturbation of the Kerr spacetime in an external region, 2009 | arXiv
[3] The Global Nonlinear Stability of the Minkowski Space, Princeton Mathematical Series, vol. 41, 1993
[4] A proof of the uniform boundedness of solutions to the wave equation on slowly rotating Kerr backgrounds, 2008 | arXiv
[5] The Evolution Problem in General Relativity, Progress in Mathematical Physics, vol. 25, Birkhäuser, 2002
[6] Peeling properties of asymptotically flat solutions to the Einstein vacuum equations, Classical and Quantum Gravity, Volume 20 (2003), pp. 3215-3257
[7] S. Klainerman, Linear stability of black holes – following M. Dafermos and I. Rodnianski, Bourbaki Seminar, 2009.
[8] Polyhomogeneity and zero rest mass fields with applications to Newman–Penrose constants, Classical and Quantum Gravity, Volume 17 (2000), pp. 605-621
[9] The peeling in the “very external region” of nonlinear perturbations of the Kerr spacetime | arXiv
[10] General Relativity, University of Chicago Press, 1984
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