Kerr stability in external regions

2023/03/22 by Dawei Shen, Shen, Dawei
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.2303.12758

openalex publication_date 2023/03/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In 2003, Klainerman and Nicolò \citeKl-Ni proved the stability of Minkowski in the case of the exterior of an outgoing null cone. Relying on the method used in \citeKl-Ni, Caciotta and Nicolò \citeCa-Ni proved the stability of Kerr spacetime in external regions, i.e. outside an outgoing null cone far away from the Kerr event horizon. In this paper, we give a new proof of \citeCa-Ni. Compared to \citeCa-Ni, we reduce the number of derivatives needed in the proof, simplify the treatment of the last slice, and provide a unified treatment of the decay of initial data which contains in particular the initial data considered by Klainerman and Szeftel in \citeKS:main. Also, concerning the treatment of curvature estimates, similar to \citeShenMink, we replace the vectorfield method used in \citeKl-Ni,Ca-Ni by r^p-weighted estimates introduced by Dafermos and Rodnianski in \citeDa-Ro.

Related

• Stability of Minkowski spacetime in exterior regions
• The peeling in the "very external region" of non linear perturbations of the Kerr spacetime
• The non linear perturbation of the Kerr spacetime in an external region
• Exterior stability of Minkowski spacetime with borderline decay
• Decay for solutions of the wave equation on Kerr exterior spacetimes III: The full subextremal case |a| < M