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A Non-degenerate Scattering Theory for the Wave Equation on Extremal Reissner–Nordström

Angelopoulos, Yannis and Aretakis, Stefanos and Gajic, Dejan (2020) A Non-degenerate Scattering Theory for the Wave Equation on Extremal Reissner–Nordström. Communications in Mathematical Physics, 380 (1). pp. 323-408. ISSN 0010-3616. PMCID PMC7591141.

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It is known that sub-extremal black hole backgrounds do not admit a (bijective) non-degenerate scattering theory in the exterior region due to the fact that the redshift effect at the event horizon acts as an unstable blueshift mechanism in the backwards direction in time. In the extremal case, however, the redshift effect degenerates and hence yields a much milder blueshift effect when viewed in the backwards direction. In this paper, we construct a definitive (bijective) non-degenerate scattering theory for the wave equation on extremal Reissner–Nordström backgrounds. We make use of physical-space energy norms which are non-degenerate both at the event horizon and at null infinity. As an application of our theory we present a construction of a large class of smooth, exponentially decaying modes. We also derive scattering results in the black hole interior region.

Item Type:Article
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URLURL TypeDescription CentralArticle Paper
Gajic, Dejan0000-0002-8194-7145
Additional Information:© 2020 The Author(s). This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit Received 04 January 2020; Accepted 13 June 2020; Published 23 September 2020. The second author (S.A.) acknowledges support through NSERC grant 502581, an Alfred P. Sloan Fellowship in Mathematics and the Connaught Fellowship 503071.
Funding AgencyGrant Number
Natural Sciences and Engineering Research Council of Canada (NSERC)502581
Alfred P. Sloan FoundationUNSPECIFIED
Natural Sciences and Engineering Research Council of Canada (NSERC)503071
University of TorontoUNSPECIFIED
Issue or Number:1
PubMed Central ID:PMC7591141
Record Number:CaltechAUTHORS:20200929-133458457
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Official Citation:Angelopoulos, Y., Aretakis, S. & Gajic, D. A Non-degenerate Scattering Theory for the Wave Equation on Extremal Reissner–Nordström. Commun. Math. Phys. 380, 323–408 (2020).
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:105642
Deposited By: Tony Diaz
Deposited On:29 Sep 2020 20:47
Last Modified:04 Nov 2020 18:50

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