| Description |
1 online resource (v, 113 pages) |
| Series |
Memoirs of the American Mathematical Society, 0065-9266 ; volume 247, number 1170 |
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Memoirs of the American Mathematical Society ; no. 1170.
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| Contents |
Chapter 1. Introduction Chapter 2. Kerr-Newman-de-Sitter black holes Chapter 3. The massless charged Dirac equation Chapter 4. The direct scattering problem Chapter 5. Uniqueness results in the inverse scattering problem at fixed energy Chapter 6. The angular equation and partial inverse result Chapter 7. The radial equation: complexification of the angular momentum Chapter 8. Large z asymptotics of the scattering data Chapter 9. The inverse scattering problem Appendix A. Growth estimate of the eigenvalues \muk Appendix B. Limiting Absorption Principles and scattering theory for H₀ and H |
| Summary |
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 |
| Notes |
"Volume 247, number 1170 (third of 7 numbers), May 2017." |
| Bibliography |
Includes bibliographical references (pages 111-113) |
| Notes |
Keywords:Inverse scattering, black holes, Dirac equation |
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Print version record |
| Subject |
Kerr black holes.
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Black holes (Astronomy)
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Inverse scattering transform.
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Dirac equation.
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SCIENCE -- Astronomy.
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Black holes (Astronomy)
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Dirac equation
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Inverse scattering transform
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Kerr black holes
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| Form |
Electronic book
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| Author |
Nicoleau, François, 1965- author.
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American Mathematical Society, publisher
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| ISBN |
9781470437015 |
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1470437015 |
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