# Time-Translation Invariance of Scattering Maps and Blue-Shift Instabilities on Kerr Black Hole Spacetimes

## Author(s): Dafermos, Mihalis; Shlapentokh-Rothman, Yakov M.

To refer to this page use: http://arks.princeton.edu/ark:/88435/pr11m19
DC FieldValueLanguage
dc.contributor.authorDafermos, Mihalis-
dc.contributor.authorShlapentokh-Rothman, Yakov M.-
dc.date.accessioned2017-11-21T19:22:29Z-
dc.date.available2017-11-21T19:22:29Z-
dc.date.issued2017-03en_US
dc.identifier.citationDafermos, Mihalis, Shlapentokh-Rothman, Yakov. (2017). Time-Translation Invariance of Scattering Maps and Blue-Shift Instabilities on Kerr Black Hole Spacetimes. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 350 (985 - 1016. doi:10.1007/s00220-016-2771-zen_US
dc.identifier.issn0010-3616-
dc.identifier.urihttp://arks.princeton.edu/ark:/88435/pr11m19-
dc.description.abstractIn this paper, we provide an elementary, unified treatment of two distinct blue-shift instabilities for the scalar wave equation on a fixed Kerr black hole background: the celebrated blue-shift at the Cauchy horizon (familiar from the strong cosmic censorship conjecture) and the time-reversed red-shift at the event horizon (relevant in classical scattering theory). Our first theorem concerns the latter and constructs solutions to the wave equation on Kerr spacetimes such that the radiation field along the future event horizon vanishes and the radiation field along future null infinity decays at an arbitrarily fast polynomial rate, yet, the local energy of the solution is infinite near any point on the future event horizon. Our second theorem constructs solutions to the wave equation on rotating Kerr spacetimes such that the radiation field along the past event horizon (extended into the black hole) vanishes and the radiation field along past null infinity decays at an arbitrarily fast polynomial rate, yet, the local energy of the solution is infinite near any point on the Cauchy horizon. The results make essential use of the scattering theory developed in Dafermos, Rodnianski and Shlapentokh-Rothman (A scattering theory for the wave equation on Kerr black hole exteriors (2014). arXiv:1412.8379) and exploit directly the time-translation invariance of the scattering map and the non-triviality of the transmission map.en_US
dc.format.extent985 - 1016en_US
dc.language.isoenen_US
dc.relation.ispartofCOMMUNICATIONS IN MATHEMATICAL PHYSICSen_US
dc.rightsAuthor's manuscripten_US
dc.titleTime-Translation Invariance of Scattering Maps and Blue-Shift Instabilities on Kerr Black Hole Spacetimesen_US
dc.typeJournal Articleen_US
dc.identifier.doidoi:10.1007/s00220-016-2771-z-
dc.date.eissued2016-10-18en_US
dc.identifier.eissn1432-0916-
pu.type.symplectichttp://www.symplectic.co.uk/publications/atom-terms/1.0/journal-articleen_US

Files in This Item:
File Description SizeFormat