Construction of GCM hypersurfaces in perturbations of Kerr

2022/05/20 by Dawei Shen, Shen, Dawei · 4 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geometric Analysis and Curvature Flows #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2205.12336

openalex publication_date 2022/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This is a follow-up of \citeKS:Kerr1 on the general covariant modulated (GCM) procedure in perturbations of Kerr. In this paper, we construct GCM hypersurfaces, which play a central role in extending GCM admissible spacetimes in \citeKS:main where decay estimates are derived in the context of nonlinear stability of Kerr family for |a|≪ m. As in \citeKS, the central idea of the construction of GCM hypersurfaces is to concatenate a 1--parameter family of GCM spheres of \citeKS:Kerr1 by solving an ODE system. The goal of this paper is to get rid of the symmetry restrictions in the GCM procedure introduced in \citeKS and thus remove an essential obstruction in extending the results to a full stability proof of the Kerr family.

Cited by

• Einstein-Maxwell Equations on Mass-Centered GCM Hypersurfaces
• Mass-Centered GCM Framework in Perturbations of Kerr(-Newman)
• Elliptic curvature estimates for linearised gravitational perturbations of Kerr in the full sub-extremal range |a|
• Linear stability of Kerr black holes in the full subextremal range

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• Effective results on uniformization and intrinsic GCM spheres in perturbations of Kerr
• Mass-Centered GCM Framework in Perturbations of Kerr(-Newman)
• Einstein-Maxwell Equations on Mass-Centered GCM Hypersurfaces
• The wave equation on subextremal Kerr spacetimes with small non-decaying first order terms