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dc.contributor.authorKehle, Christophen
dc.contributor.authorShlapentokh-Rothman, Yakoven
dc.date.accessioned2019-02-09T00:31:41Z
dc.date.available2019-02-09T00:31:41Z
dc.date.issued2019-05en
dc.identifier.issn1424-0637
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/289085
dc.description.abstractWe develop a scattering theory for the linear wave equation □ψ=0 on the interior of Reissner-Nordström black holes, connecting the fixed frequency picture to the physical space picture. Our main result gives the existence, uniqueness and asymptotic completeness of finite energy scattering states. The past and future scattering states are represented as suitable traces of the solution ψ on the bifurcate event and Cauchy horizons. The heart of the proof is to show that after separation of variables one has uniform boundedness of the reflection and transmission coefficients of the resulting radial o.d.e. over all frequencies ω and ℓ. This is non-trivial because the natural T conservation law is sign-indefinite in the black hole interior. In the physical space picture, our results imply that the Cauchy evolution from the event horizon to the Cauchy horizon is a Hilbert space isomorphism, where the past (resp. future) Hilbert space is defined by the finiteness of the degenerate T energy fluxes on both components of the event (resp. Cauchy) horizon. Finally, we prove that, in contrast to the above, for a generic set of cosmological constants Λ, there is no analogous finite T energy scattering theory for either the linear wave equation or the Klein-Gordon equation with conformal mass on the (anti-) de Sitter-Reissner-Nordström interior.
dc.languageenen
dc.publisherBirkhauser Verlag
dc.titleA Scattering Theory for Linear Waves on the Interior of Reissner–Nordström Black Holesen
dc.typeArticle
prism.endingPage1650
prism.issueIdentifier5en
prism.publicationDate2019en
prism.publicationNameAnnales Henri Poincaréen
prism.startingPage1583
prism.volume20en
dc.identifier.doi10.17863/CAM.36347
rioxxterms.versionofrecord10.1007/s00023-019-00760-zen
rioxxterms.versionAM
rioxxterms.licenseref.urihttp://www.rioxx.net/licenses/all-rights-reserveden
rioxxterms.licenseref.startdate2019-05en
dc.identifier.eissn1424-0661
rioxxterms.typeJournal Article/Reviewen
cam.issuedOnline2019-02-13en
cam.orpheus.successThu Jan 30 10:51:26 GMT 2020 - Embargo updated*
rioxxterms.freetoread.startdate2020-02-01


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