Burnett’s conjecture in general relativity

Arthur Touati

doi:10.5802/crmeca.288

Review article

Burnett’s conjecture in general relativity

Arthur Touati ¹

¹ CNRS & IMB, Bordeaux University, France

Comptes Rendus. Mécanique, Volume 353 (2025), pp. 455-476.

This article is part of the thematic issue Recent advances in general relativity: an issue in memory of Yvonne Choquet-Bruhat edited by Jérémie Szeftel.

Abstract
Résumé

We present the literature on Burnett’s conjecture in general relativity, which relate weak limits of vacuum solutions to relativistic kinetic theory. A special care is put on relating these works with early Choquet-Bruhat’s results on high-frequency gravitational waves and geometric optics.

Nous passons en revue la littérature sur la conjecture de Burnett en relativité générale, qui relie les limites faibles des solutions du vide à la théorie cinétique relativiste. Une attention particulière est portée sur le lien entre ces travaux et les premiers résultats de Choquet-Bruhat concernant les ondes gravitationnelles haute fréquence et l’optique géométrique.

Received: 2024-11-22
Revised: 2025-02-03
Accepted: 2025-02-06
Published online: 2025-02-20

DOI: 10.5802/crmeca.288

Keywords: Einstein equations, Backreaction, Relativistic kinetic theory, Compensated compactness, Geometric optics, High-frequency gravitational waves
Mots-clés : Équations d’Einstein, Rétroaction, Théorie cinétique relativiste, Compacité compensée, Optique géométrique, Ondes gravitationnelles haute fréquence

Author's affiliations:

Arthur Touati ¹

¹ CNRS & IMB, Bordeaux University, France

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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Arthur Touati. Burnett’s conjecture in general relativity. Comptes Rendus. Mécanique, Volume 353 (2025), pp. 455-476. doi : 10.5802/crmeca.288. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.288/

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