The stability of Minkowski space and its influence on the mathematical analysis of General Relativity

Jacques Smulevici

doi:10.5802/crmeca.287

Article de synthèse

The stability of Minkowski space and its influence on the mathematical analysis of General Relativity
[La stabilité de l’espace de Minkowski et son influence sur l’analyse mathématique de la Relativité Générale]

Jacques Smulevici ¹

¹ Laboratoire Jacques-Louis Lions (LJLL), Sorbonne Université, CNRS and Institut Universitaire de France, France

Comptes Rendus. Mécanique, Volume 353 (2025), pp. 519-542.

Cet article fait partie du numéro thématique Avancées récentes dans le domaine de la relativité générale : numéro en l'honneur d'Yvonne Choquet-Bruhat coordonné par Jérémie Szeftel.

Résumé
Abstract

L’étude de la stabilité de l’espace de Minkowski a eu une influence majeure sur l’analyse mathématique de la Relativité Générale et, plus largement, sur les équations aux dérivées partielles hyperboliques géométriques. Cet article propose un aperçu du contexte, des idées et d’une partie de l’héritage entourant ce sujet, en mettant particulièrement l’accent sur la démonstration originale de Christodoulou–Klainerman.

The study of the stability of Minkowksi space has had a tremendous influence on the mathematical analysis of General Relativity and in a wider context, on geometric hyperbolic partial differential equations. This article proposes an overview of the context, ideas and part of the legacy surrounding this subject, focusing particularly on the original proof of Christodoulou–Klainerman.

Reçu le : 2024-10-30
Révisé le : 2025-01-31
Accepté le : 2025-02-06
Publié le : 2025-03-27

DOI : 10.5802/crmeca.287

Keywords: Einstein equations, General Relativity, Asymptotic stability
Mots-clés : Équations d’Einstein, Relativité Générale, Stabilité asymptotique

Affiliations des auteurs :

Jacques Smulevici ¹

¹ Laboratoire Jacques-Louis Lions (LJLL), Sorbonne Université, CNRS and Institut Universitaire de France, France

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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Jacques Smulevici. The stability of Minkowski space and its influence on the mathematical analysis of General Relativity. Comptes Rendus. Mécanique, Volume 353 (2025), pp. 519-542. doi : 10.5802/crmeca.287. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.287/

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