Non linear stability of einsteinian spacetimes with U(1) isometry group

2003/02/07 by Yvonne Choquet–Bruhat, Yvonne Choquet-Bruhat, Choquet-Bruhat, Yvonne +2 · 1 citation
Earth and Planetary Sciences · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High-pressure geophysics and materials #gr-qc

paper · pdf · doi:10.48550/arxiv.gr-qc/0302021

Conference in honor of J. Leray, Tokyo 2001, Kajitani and Vaillant ed. to appear Birkhauser

arxiv created 2003/02/07 · openalex publication_date 2003/02/07 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove global completeness in the expanding direction of spacetimes satisfying the vacuum Einstein equations on a manifold of the form Σ× S¹× R where Σ is a compact surface of genus G>1. The Cauchy data are supposed to be invariant with respect to the group S¹ and sufficiently small, but we do not impose a restrictive hypothesis made in gr-qc 0112049 on the lowest eigenvalue of a relevant Laplacian. The total energy decay still holds, but its rate depends of the asymptotic value of this eigenvalue.

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