Initial data for the Einstein equations must satisfy a system of nonlinear partial differential equations, the Einstein constraint equations. Constructing interesting solutions of the constraint equations can then lead to interesting spacetime evolutions. Over the past twenty-five years, various gluing methods to construct solutions of the constraints have shed light on some long-standing questions. In this article we survey some of the methods and results achieved to date.
Les données initiales des équations d’Einstein doivent satisfaire un système d’équations aux dérivées partielles non linéaires, les équations de contrainte d’Einstein. La construction de solutions intéressantes des équations de contrainte peut alors conduire à des évolutions intéressantes de l’espace-temps. Au cours des vingt-cinq dernières années, diverses méthodes de recollement permettant de construire des solutions des équations de contrainte ont permis de faire la lumière sur certaines questions de longue date. Dans cet article, nous passons en revue quelques-unes des méthodes et des résultats obtenus à ce jour.
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Mots-clés : Equations de contrainte d’ Einstein, Analyse géométrique, Méthodes de recollement
Justin Corvino 1
CC-BY 4.0
@article{CRMECA_2025__353_G1_29_0,
author = {Justin Corvino},
title = {Gluing for the {Einstein} constraint equations},
journal = {Comptes Rendus. M\'ecanique},
pages = {29--52},
publisher = {Acad\'emie des sciences, Paris},
volume = {353},
year = {2025},
doi = {10.5802/crmeca.275},
language = {en},
}
Justin Corvino. Gluing for the Einstein constraint equations. Comptes Rendus. Mécanique, Volume 353 (2025), pp. 29-52. doi : 10.5802/crmeca.275. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.275/
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