Inverse scattering at fixed energy for massive charged Dirac fields in de Sitter-Reissner-Nordstr\'om black holes
| Autor: | Gobin, Damien |
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| Rok vydání: | 2014 |
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| Druh dokumentu: | Working Paper |
| Popis: | In this paper, we consider massive charged Dirac fields propagating in the exterior region of de Sitter-Reissner-Nordstr\"om black holes.We show that the parameters of such black holes are uniquely determined by the partial knowledge of the corresponding scattering operator $S(\lambda)$ at a fixed energy $\lambda$.More precisely, we consider the partial wave scattering operators $S(\lambda,n)$ (here $\lambda \in \mathbb{R}$ is the energy and $n \in \mathbb{N}^{\star}$ denotes the angular momentum) defined as the restrictions of the full scattering operator on a well chosen basis of spin-weighted spherical harmonics.We prove that the knowledge of the scattering operators $S(\lambda,n)$, for all $n \in \mathcal{L}$, where $\mathcal{L}$ is a subset of $\mathbb{N}^{\star}$ that satisfies the M\"untz condition $\sum\_{n \in \mathcal{L}} \frac{1}{n} = + \infty$, allows to recover the mass, the charge and the cosmological constant of a dS-RN black hole.The main tool consists in the complexification of the angular momentum $n$ and in studying the analytic properties of the "unphysical" corresponding data in the complex variable $z$. Comment: arXiv admin note: text overlap with arXiv:1004.1466, arXiv:0904.2064 by other authors |
| Databáze: | arXiv |
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