34
IRUS TotalDownloads
Altmetric
Conservation laws and flux bounds for gravitational perturbations of the Schwarzschild metric
File | Description | Size | Format | |
---|---|---|---|---|
conslaw16aug9.pdf | Accepted version | 273.98 kB | Adobe PDF | View/Open |
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 Faculty of Natural Sciences Mathematics |