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Direct and inverse scattering at fixed energy for massless charged Dirac fields by Kerr-Newman-de Sitter black holes /
In this paper, we 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, we establish the existence and asymptotic completeness of time-dependent wave operators associa...
| Clasificación: | Libro Electrónico |
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| Autores principales: | , |
| Formato: | Documento de Gobierno Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence, Rhode Island :
American Mathematical Society,
2017.
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| Colección: | Memoirs of the American Mathematical Society ;
no. 1170. |
| Temas: | |
| Acceso en línea: | Texto completo |
| Sumario: | In this paper, we 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, we 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. We 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, we 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, we are finally able to determine uniquely the metric of the black hole from the knowledge of the scattering matrix at a fixed energy. |
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| Notas: | "Volume 247, number 1170 (third of 7 numbers), May 2017." Keywords:Inverse scattering, black holes, Dirac equation. |
| Descripción Física: | 1 online resource (v, 113 pages) |
| Bibliografía: | Includes bibliographical references (pages 111-113). |
| ISBN: | 9781470437015 1470437015 |
| ISSN: | 0065-9266 ; |