دورية أكاديمية
Inverse scattering at fixed energy in de Sitter-Reissner-Nordström black holes
| العنوان: | Inverse scattering at fixed energy in de Sitter-Reissner-Nordström black holes |
|---|---|
| المؤلفون: | Daudé, Thierry, Nicoleau, François |
| المساهمون: | McGill University = Université McGill Montréal, Canada, Laboratoire de Mathématiques Jean Leray (LMJL), Centre National de la Recherche Scientifique (CNRS)-Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Université de Nantes (UN)-Université de Nantes (UN) |
| المصدر: | ISSN: 1424-0637. |
| بيانات النشر: | HAL CCSD Springer Verlag |
| سنة النشر: | 2011 |
| المجموعة: | Archive ouverte HAL (Hyper Article en Ligne, CCSD - Centre pour la Communication Scientifique Directe) |
| مصطلحات موضوعية: | Black holes, Inverse scattering, Dirac equation, 81U40 35P25, [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph], [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph] |
| الوصف: | 40 pages ; In this paper, we consider massless Dirac fields propagating in the outer region of de Sitter-Reissner-Nordström black holes. We show that the metric of such black holes is uniquely determined by the partial knowledge of the corresponding scattering matrix $S(\lambda)$ at a fixed energy $\lambda \ne 0$. More precisely, we consider the partial wave scattering matrices $S(\lambda,n)$ (here $\lambda \ne 0$ is the fixed energy and $n \in \N^*$ denotes the angular momentum) defined as the restrictions of the full scattering matrix on a well chosen basis of spin-weighted spherical harmonics. We prove that the mass $M$, the square of the charge $Q^2$ and the cosmological constant $\Lambda$ of a dS-RN black hole (and thus its metric) can be uniquely determined from the knowledge of either the transmission coefficients $T(\lambda, n)$, or the reflexion coefficients $R(\lambda, n)$ (resp. $L(\lambda, n)$), for all $n \in {\mathcal{L}}$ where $\mathcal{L}$ is a subset of $\N^*$ that satisfies the Müntz condition $\sum_{n \in {\mathcal{L}}} \frac{1}{n} = +\infty$. Our main tool consists in complexifying the angular momentum $n$ and in studying the analytic properties of the "unphysical" scattering matrix $S(\lambda,z)$ in the complex variable $z$. We show in particular that the quantities $\frac{1}{T(\lambda,z)}$, $\frac{R(\lambda,z)}{T(\lambda,z)}$ and $\frac{L(\lambda,z)}{T(\lambda,z)}$ belong to the Nevanlinna class in the region $\{z \in \C, \ Re(z) >0 \}$ for which we have analytic uniqueness theorems at our disposal. Eventually, as a by-product of our method, we obtain reconstrution formulae for the surface gravities of the event and cosmological horizons of the black hole which have an important physical meaning in the Hawking effect. |
| نوع الوثيقة: | article in journal/newspaper |
| اللغة: | English |
| العلاقة: | info:eu-repo/semantics/altIdentifier/arxiv/1004.1466; hal-00470157; https://hal.archives-ouvertes.fr/hal-00470157Test; https://hal.archives-ouvertes.fr/hal-00470157/documentTest; https://hal.archives-ouvertes.fr/hal-00470157/file/DaudeNicoleau-Fixed-dS-RN.pdfTest; ARXIV: 1004.1466 |
| الإتاحة: | https://hal.archives-ouvertes.fr/hal-00470157Test https://hal.archives-ouvertes.fr/hal-00470157/documentTest https://hal.archives-ouvertes.fr/hal-00470157/file/DaudeNicoleau-Fixed-dS-RN.pdfTest |
| حقوق: | info:eu-repo/semantics/OpenAccess |
| رقم الانضمام: | edsbas.6330FCA2 |
| قاعدة البيانات: | BASE |
| الوصف غير متاح. |