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dc.contributor.authorHolzegel, Gustav
dc.contributor.authorLuk, Jonathan
dc.contributor.authorSmulevici, Jacques
dc.contributor.authorWarnick, Claude
dc.date.accessioned2021-09-13T23:31:35Z
dc.date.available2021-09-13T23:31:35Z
dc.date.issued2020
dc.identifier.issn0010-3616
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/327957
dc.description.abstractWe study the global dynamics of the wave equation, Maxwell's equation and the linearized Bianchi equations on a fixed anti-de Sitter (AdS) background. Provided dissipative boundary conditions are imposed on the dynamical fields we prove uniform boundedness of the natural energy as well as both degenerate (near the AdS boundary) and non-degenerate integrated decay estimates. Remarkably, the non-degenerate estimates "lose a derivative". We relate this loss to a trapping phenomenon near the AdS boundary, which itself originates from the properties of (approximately) gliding rays near the boundary. Using the Gaussian beam approximation we prove that non-degenerate energy decay without loss of derivatives does not hold. As a consequence of the non-degenerate integrated decay estimates, we also obtain pointwise-in-time decay estimates for the energy. Our paper provides the key estimates for a proof of the non-linear stability of the anti-de Sitter spacetime under dissipative boundary conditions. Finally, we contrast our results with the case of reflecting boundary conditions.
dc.publisherSpringer Science and Business Media LLC
dc.rightsAttribution 4.0 International
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subjectgr-qc
dc.subjectgr-qc
dc.subjectmath-ph
dc.subjectmath.AP
dc.subjectmath.MP
dc.titleAsymptotic properties of linear field equations in anti-de Sitter space
dc.typeArticle
prism.publicationNamearXiv
dc.identifier.doi10.17863/CAM.75410
dcterms.dateAccepted2019-08-18
rioxxterms.versionofrecord10.1007/s00220-019-03601-6
rioxxterms.versionVoR
rioxxterms.licenseref.urihttp://www.rioxx.net/licenses/all-rights-reserved
rioxxterms.licenseref.startdate2019-08-18
dc.contributor.orcidWarnick, Claude [0000-0001-7132-8319]
dc.identifier.eissn1432-0916
dc.publisher.urlarxiv:1502.04965
rioxxterms.typeJournal Article/Review
cam.issuedOnline2019-11-04
dc.identifier.urlarxiv:1502.04965


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Attribution 4.0 International
Except where otherwise noted, this item's licence is described as Attribution 4.0 International