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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 |
|---|---|
| Autores principales: | , |
| Formato: | Documento de Gobierno Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence, Rhode Island :
American Mathematical Society,
2017.
|
| Colección: | Memoirs of the American Mathematical Society ;
no. 1170. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 020 | |z 1470423766 |q (alk. paper) | ||
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| 049 | |a UAMI | ||
| 100 | 1 | |a Daudé, Thierry, |d 1977- |e author. |1 https://id.oclc.org/worldcat/entity/E39PCjMy4h96YDCpcyYyJB7Dtq | |
| 245 | 1 | 0 | |a Direct and inverse scattering at fixed energy for massless charged Dirac fields by Kerr-Newman-de Sitter black holes / |c Thierry Daudé, François Nicoleau. |
| 264 | 1 | |a Providence, Rhode Island : |b American Mathematical Society, |c 2017. | |
| 264 | 4 | |c ©2016 | |
| 300 | |a 1 online resource (v, 113 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Memoirs of the American Mathematical Society, |x 0065-9266 ; |v volume 247, number 1170 | |
| 500 | |a "Volume 247, number 1170 (third of 7 numbers), May 2017." | ||
| 504 | |a Includes bibliographical references (pages 111-113). | ||
| 500 | |a Keywords:Inverse scattering, black holes, Dirac equation. | ||
| 505 | 0 | 0 | |g Chapter 1. |t Introduction |g Chapter 2. |t Kerr-Newman-de-Sitter black holes |g Chapter 3. |t The massless charged Dirac equation |g Chapter 4. |t The direct scattering problem |g Chapter 5. |t Uniqueness results in the inverse scattering problem at fixed energy |g Chapter 6. |t The angular equation and partial inverse result |g Chapter 7. |t The radial equation: complexification of the angular momentum |g Chapter 8. |t Large z asymptotics of the scattering data |g Chapter 9. |t The inverse scattering problem |g Appendix A. |t Growth estimate of the eigenvalues \muk |g Appendix B. |t Limiting Absorption Principles and scattering theory for H₀ and H. |
| 520 | 3 | |a 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. | |
| 588 | 0 | |a Print version record. | |
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Kerr black holes. | |
| 650 | 0 | |a Black holes (Astronomy) | |
| 650 | 0 | |a Inverse scattering transform. | |
| 650 | 0 | |a Dirac equation. | |
| 650 | 6 | |a Kerr, Trous noirs de. | |
| 650 | 6 | |a Trous noirs (Astronomie) | |
| 650 | 6 | |a Problème inverse de diffusion. | |
| 650 | 6 | |a Équation de Dirac. | |
| 650 | 7 | |a SCIENCE |x Astronomy. |2 bisacsh | |
| 650 | 7 | |a Black holes (Astronomy) |2 fast | |
| 650 | 7 | |a Dirac equation |2 fast | |
| 650 | 7 | |a Inverse scattering transform |2 fast | |
| 650 | 7 | |a Kerr black holes |2 fast | |
| 700 | 1 | |a Nicoleau, François, |d 1965- |e author. |1 https://id.oclc.org/worldcat/entity/E39PCjyDFdchvwctKpqgk3H6cd | |
| 710 | 2 | |a American Mathematical Society, |e publisher. | |
| 758 | |i has work: |a Direct and inverse scattering at fixed energy for massless charged Dirac fields by Kerr-Newman-de Sitter black holes (Text) |1 https://id.oclc.org/worldcat/entity/E39PCFBDqmFWhvpWDM8gFjJFKd |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Daudé, Thierry, 1977- |t Direct and inverse scattering at fixed energy for massless charged Dirac fields by Kerr-Newman-de Sitter black holes |z 9781470423766 |w (DLC) 2017010089 |w (OCoLC)973917354 |
| 830 | 0 | |a Memoirs of the American Mathematical Society ; |v no. 1170. | |
| 856 | 4 | 0 | |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=4908292 |z Texto completo |
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