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ISBN: 0198520506 Year: 1983 Publisher: Oxford : Clarendon Press Oxford University Press,
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Black holes (Astronomy) --- Kerr black holes. --- Space and time --- Mathematics --- Mathematics. --- BLACK HOLES (ASTRONOMY) --- KERR BLACK HOLES --- SPACE AND TIME --- MATHEMATICS
Book
ISBN: 1470437015 Year: 2017 Publisher: Providence, Rhode Island : American Mathematical Society,
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In 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.
Kerr black holes. --- Black holes (Astronomy) --- Inverse scattering transform. --- Dirac equation.
ISBN: 0198512910 Year: 1983 Volume: 69 Publisher: Oxford
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Cosmology --- Theory of relativity. Unified field theory --- Stars --- Mathematical physics --- Black holes (Astronomy) --- Trous noirs (Astronomie) --- 524.8 --- -Kerr black holes --- Space and time --- -Space of more than three dimensions --- Space-time --- Space-time continuum --- Space-times --- Spacetime --- Time and space --- Fourth dimension --- Infinite --- Metaphysics --- Philosophy --- Space sciences --- Time --- Beginning --- Hyperspace --- Relativity (Physics) --- Frozen stars --- Compact objects (Astronomy) --- Gravitational collapse --- The Universe. Metagalaxy. Cosmology --- Mathematics --- Kerr black holes. --- Mathematics. --- 524.8 The Universe. Metagalaxy. Cosmology --- -The Universe. Metagalaxy. Cosmology --- -Fourth dimension --- Space of more than three dimensions --- -Black holes (Astronomy) --- -524.8 The Universe. Metagalaxy. Cosmology --- Kerr black holes --- BLACK HOLES (ASTRONOMY) --- KERR BLACK HOLES --- SPACE AND TIME --- MATHEMATICS
ISBN: 9780198503705 0198503709 Year: 2009 Publisher: Oxford: Clarendon,
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ISBN: 9781470423766 Year: 2017 Publisher: Providence, Rhode Island : American Mathematical Society,
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Kerr black holes --- Black holes (Astronomy) --- Inverse scattering transform. --- Dirac equation. --- Kerr, Trous noirs de --- Trous noirs (Astronomie) --- Inverse scattering transform --- Dirac, Equation de --- Dirac equation --- kerr, Effet --- Trous noirs (astronomie) --- Problème inverse de diffusion --- Kerr, Effet. --- Dirac, Équation de. --- Problème inverse de diffusion.
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