Boundedness and decay for the Teukolsky equation on Kerr spacetimes I:\n the case |a|\≪ M

2017/11/21 by Mihalis Dafermos, Dafermos, Mihalis, Gustav Holzegel +3
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Mathematical Physics (math-ph) #Nonlinear Photonic Systems #Quantum Chromodynamics and Particle Interactions

paper · pdf · doi:10.48550/arxiv.1711.07944

openalex publication_date 2017/11/21 · openalex created_date 2022/08/15 · openalex updated_date 2026/07/28

Abstract

We prove boundedness and polynomial decay statements for solutions of the\nspin \±2 Teukolsky equation on a Kerr exterior background with parameters\nsatisfying |a|\≪ M. The bounds are obtained by introducing generalisations\nof the higher order quantities P and underlineP used in our previous\nwork on the linear stability of Schwarzschild. The existence of these\nquantities in the Schwarzschild case is related to the transformation theory of\nChandrasekhar. In a followup paper, we shall extend this result to the general\nsub-extremal range of parameters |a|<M. As in the Schwarzschild case, these\nbounds provide the first step in proving the full linear stability of the Kerr\nmetric to gravitational perturbations.\n

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