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

Title: Boundedness and decay for the Teukolsky equation on Kerr spacetimes I: the case |a|≪M
Authors: Holzegel, G
Dafermos, M
Rodnianski, I
Item Type: Journal Article
Abstract: We prove boundedness and polynomial decay statements for solutions of the spin ±2 Teukolsky equation on a Kerr exterior background with parameters satisfying |a|≪M . The bounds are obtained by introducing generalisations of the higher order quantities P and P–– used in our previous work on the linear stability of Schwarzschild. The existence of these quantities in the Schwarzschild case is related to the transformation theory of Chandrasekhar. In a followup paper, we shall extend this result to the general sub-extremal range of parameters |a|<M . As in the Schwarzschild case, these bounds provide the first step in proving the full linear stability of the Kerr metric to gravitational perturbations.
Issue Date: 1-Jun-2019
Date of Acceptance: 15-Dec-2018
URI: http://hdl.handle.net/10044/1/76577
DOI: 10.1007/s40818-018-0058-8
ISSN: 2524-5317
Publisher: Springer
Start Page: 1
End Page: 118
Journal / Book Title: Annals of PDE
Volume: 5
Issue: 1
Copyright Statement: © The Author(s) 2019. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Sponsor/Funder: Commission of the European Communities
Funder's Grant Number: FP7-ERC-2013-StG-337488
Keywords: General relativity
Kerr black hole
Teukolsky equation
Publication Status: Published
Article Number: 2
Online Publication Date: 2019-01-08
Appears in Collections:Pure Mathematics
Faculty of Natural Sciences
Mathematics