A general formalism for the stability of Kerr

2020/02/07 by Elena Giorgi, Sergiù Klainerman, Giorgi, Elena +3 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Mathematical Physics (math-ph) #Nonlinear Photonic Systems #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2002.02740

openalex publication_date 2020/02/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The goal of this paper is to provide a geometric framework for analyzing the uniform decay properties of solutions to the Teukolsky equation in the fully nonlinear setting of perturbations of Kerr. It contains the first nonlinear version of the Chandrasekhar transformation introduced in the linearized setting in \citeD-H-R-Kerr and \citeMa with the intent to use it in our ongoing project to prove the full nonlinear stability of slowly rotating Kerr as solution to the Einstein vacuum equations.

Citations

• An Approach to Gravitational Radiation by a Method of Spin Coefficients

Cited by

• Elliptic curvature estimates for linearised gravitational perturbations of Kerr in the full sub-extremal range |a|

Related

• Brief introduction to the nonlinear stability of Kerr
• Linear stability of slowly rotating Kerr black holes
• Nonlinear stability of the slowly-rotating Kerr-de Sitter family
• Instability of the Kerr Cauchy horizon under linearised gravitational perturbations
• Boundedness and decay for the Teukolsky equation on Kerr spacetimes I:\n the case |a|\≪ M