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Conservation laws and flux bounds for gravitational perturbations of the Schwarzschild metric

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Title: Conservation laws and flux bounds for gravitational perturbations of the Schwarzschild metric
Authors: Holzegel, G
Item Type: Journal Article
Abstract: We derive an energy conservation law for the system of gravitational perturbations on the Schwarzschild spacetime expressed in a double null gauge. The resulting identity involves only first derivatives of the metric perturbation. Exploiting the gauge invariance up to boundary terms of the fluxes that appear, we are able to establish positivity of the flux on any outgoing null hypersurface to the future of the initial data. This allows us to bound the total energy flux through any such hypersurface, including the event horizon, in terms of initial data. We similarly bound the total energy radiated to null infinity. Our estimates provide a direct approach to a weak form of stability, thereby complementing the proof of the full linear stability of the Schwarzschild solution recently obtained in Dafermos et al (2016 The linear stability of the Schwarzschild solution to gravitational perturbations arXiv:1601.06467).
Issue Date: 20-Sep-2016
Date of Acceptance: 15-Aug-2016
URI: http://hdl.handle.net/10044/1/39549
DOI: http://dx.doi.org/10.1088/0264-9381/33/20/205004
ISSN: 1361-6382
Publisher: IOP Publishing
Journal / Book Title: Classical and Quantum Gravity
Volume: 33
Issue: 20
Copyright Statement: © 2016 IOP Publishing Ltd. This is an author-created, un-copyedited version of an article accepted for publication in Classical and Quantum Gravity. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The definitive publisher authenticated version is available online at http://dx.doi.org/10.1088/0264-9381/33/20/205004
Sponsor/Funder: Commission of the European Communities
Funder's Grant Number: FP7-ERC-2013-StG-337488
Keywords: Science & Technology
Physical Sciences
Astronomy & Astrophysics
Physics, Multidisciplinary
Physics, Particles & Fields
Physics
stability
canonical energy
Schwarzschild spacetime
BLACK-HOLE
SPACE-TIMES
STABILITY
RADIATION
Nuclear & Particles Physics
Mathematical Sciences
Publication Status: Published
Article Number: 205004
Appears in Collections:Pure Mathematics
Mathematics
Faculty of Natural Sciences



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