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Unique Continuation from Infinity in Asymptotically Anti-de Sitter Spacetimes

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Title: Unique Continuation from Infinity in Asymptotically Anti-de Sitter Spacetimes
Authors: Holzegel, G
Shao, A
Item Type: Journal Article
Abstract: We consider the unique continuation properties of asymptotically Anti-de Sitter spacetimes by studying Klein-Gordon-type equations gφ + σφ = G(φ, ∂φ), σ ∈ R, on a large class of such spacetimes. Our main result establishes that if φ vanishes to sufficiently high order (depending on σ) on a sufficiently long time interval along the conformal boundary I, then the solution necessarily vanishes in a neighborhood of I. In particular, in the σ-range where Dirichlet and Neumann conditions are possible on I for the forward problem, we prove uniqueness if both these conditions are imposed. The length of the time interval can be related to the refocusing time of null geodesics on these backgrounds and is expected to be sharp. Some global applications as well a uniqueness result for gravitational perturbations are also discussed. The proof is based on novel Carleman estimates established in this setting.
Issue Date: 24-Feb-2016
Date of Acceptance: 7-Dec-2015
URI: http://hdl.handle.net/10044/1/29354
DOI: http://dx.doi.org/10.1007/s00220-016-2576-0
ISSN: 1432-0916
Publisher: Springer Verlag
Start Page: 723
End Page: 775
Journal / Book Title: Communications in Mathematical Physics
Volume: 347
Issue: 3
Copyright Statement: 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.
Sponsor/Funder: Commission of the European Communities
Funder's Grant Number: FP7-ERC-2013-StG-337488
Keywords: Science & Technology
Physical Sciences
Physics, Mathematical
Physics
MASSIVE WAVE-EQUATION
ADS SPACETIMES
OPERATORS
Mathematical Physics
Quantum Physics
Pure Mathematics
Publication Status: Published
Appears in Collections:Pure Mathematics
Mathematics
Faculty of Natural Sciences