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dc.contributor.authorDafermos, Mihalisen
dc.contributor.authorHolzegel, Gustaven
dc.contributor.authorRodnianski, Igoren
dc.date.accessioned2019-12-12T00:32:16Z
dc.date.available2019-12-12T00:32:16Z
dc.date.issued2019-03en
dc.identifier.issn0001-5962
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/299776
dc.description.abstractWe prove in this paper the linear stability of the celebrated Schwarzschild family of black holes in general relativity: Solutions to the linearisation of the Einstein vacuum equations around a Schwarzschild metric arising from regular initial data remain globally bounded on the black hole exterior and in fact decay to a linearised Kerr metric. We express the equations in a suitable double null gauge. To obtain decay, one must in fact add a residual pure gauge solution which we prove to be itself quantitatively controlled from initial data. Our result a fortiori includes decay statements for general solutions of the Teukolsky equation (satisfied by gauge-invariant null-decomposed curvature components). These latter statements are in fact deduced in the course of the proof by exploiting associated quantities shown to satisfy the Regge--Wheeler equation, for which appropriate decay can be obtained easily by adapting previous work on the linear scalar wave equation. The bounds on the rate of decay to linearised Kerr are inverse polynomial, suggesting that dispersion is sufficient to control the non-linearities of the Einstein equations in a potential future proof of nonlinear stability. This paper is self-contained and includes a physical-space derivation of the equations of linearised gravity around Schwarzschild from the full non-linear Einstein vacuum equations expressed in a double null gauge.
dc.publisherInstitut Mittag-Leffler
dc.rightsAll rights reserved
dc.rights.uri
dc.subjectgr-qcen
dc.subjectgr-qcen
dc.subjectmath-phen
dc.subjectmath.APen
dc.subjectmath.DGen
dc.subjectmath.MPen
dc.titleThe linear stability of the Schwarzschild solution to gravitational perturbationsen
dc.typeArticle
prism.endingPage214
prism.issueIdentifier1en
prism.publicationDate2019en
prism.publicationNameActa Mathematicaen
prism.startingPage1
prism.volume222en
dc.identifier.doi10.17863/CAM.46846
dcterms.dateAccepted2019-01-17en
rioxxterms.versionofrecord10.4310/ACTA.2019.v222.n1.a1en
rioxxterms.versionAM
rioxxterms.licenseref.urihttp://www.rioxx.net/licenses/all-rights-reserveden
rioxxterms.licenseref.startdate2019-03en
dc.identifier.eissn1871-2509
rioxxterms.typeJournal Article/Reviewen
cam.issuedOnline2019-04-05en
rioxxterms.freetoread.startdate2020-12-25


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