Einstein vacuum equations with 𝕌(1) symmetry in an elliptic gauge: Local well-posedness and blow-up criterium

Author:

Touati Arthur1

Affiliation:

1. Centre de Mathématiques Laurent Schwartz, Ecole Polytechnique, Route de Saclay, Palaiseau 91120, France

Abstract

In this paper, we are interested in the Einstein vacuum equations on a Lorentzian manifold displaying [Formula: see text] symmetry. We identify some freely prescribable initial data, solve the constraint equations and prove the existence of a unique and local in time solution at the [Formula: see text] level. In addition, we prove a blow-up criterium at the [Formula: see text] level. By doing so, we improve a result of Huneau and Luk in [Einstein equations under polarized [Formula: see text] symmetry in an elliptic gauge, Commun. Math. Phys. 361(3) (2018) 873–949] on a similar system, and our main motivation is to provide a framework adapted to the study of high-frequency solutions to the Einstein vacuum equations done in a forthcoming paper by Huneau and Luk. As a consequence we work in an elliptic gauge, particularly adapted to the handling of high-frequency solutions, which have large high-order norms.

Publisher

World Scientific Pub Co Pte Ltd

Subject

General Mathematics,Analysis

Reference11 articles.

1. The high‐frequency limit in general relativity

2. Wave Maps in General Relativity

3. Oxford Mathematical Monographs;Choquet-Bruhat Y.,2009

Cited by 2 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. High-frequency solutions to the Einstein equations;Classical and Quantum Gravity;2024-06-20

2. Geometric optics approximation for the Einstein vacuum equations;Séminaire Laurent Schwartz — EDP et applications;2023-07-12

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