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OverviewIn this paper, the authors study the direct and inverse scattering theory at fixed energy for massless charged Dirac fields evolving in the exterior region of a Kerr-Newman-de Sitter black hole. In the first part, they establish the existence and asymptotic completeness of time-dependent wave operators associated to our Dirac fields. This leads to the definition of the time-dependent scattering operator that encodes the far-field behavior (with respect to a stationary observer) in the asymptotic regions of the black hole: the event and cosmological horizons. The authors also use the miraculous property (quoting Chandrasekhar)--that the Dirac equation can be separated into radial and angular ordinary differential equations-to make the link between the time-dependent scattering operator and its stationary counterpart. This leads to a nice expression of the scattering matrix at fixed energy in terms of stationary solutions of the system of separated equations. In a second part, the authors use this expression of the scattering matrix to study the uniqueness property in the associated inverse scattering problem at fixed energy. Using essentially the particular form of the angular equation (that can be solved explicitly by Frobenius method) and the Complex Angular Momentum technique on the radial equation, the authors are finally able to determine uniquely the metric of the black hole from the knowledge of the scattering matrix at a fixed energy. Full Product DetailsAuthor: Thierry Daude , Francois NicoleauPublisher: American Mathematical Society Imprint: American Mathematical Society Weight: 0.200kg ISBN: 9781470423766ISBN 10: 1470423766 Pages: 113 Publication Date: 30 June 2017 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Out of stock  The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available. Table of ContentsIntroduction Kerr-Newman-de-Sitter black holes The massless charged Dirac equation The direct scattering problem Uniqueness results in the inverse scattering problem at fixed energy The angular equation and partial inverse result The radial equation: complexification of the angular momentum Large $z$ asymptotics of the scattering data The inverse scattering problem Appendix A. Growth estimate of the eigenvalues $\mu_{kl}(\lambda)$ Appendix B. Limiting Absorption principles and scattering theory for $H_0$ and $H$ BibliographyReviewsAuthor InformationThierry Daude, Universite de Cergy-Pontoise, France. Francois Nicoleau, Universite de Nantes, France. Tab Content 6Author Website:Countries AvailableAll regions |
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