caa a22 4500 445320176 CHVBK 20180317142701.0 cr unu---uuuuu 170323e20110201xx s 000 0 eng 10.1007/s00023-010-0069-9 doi (NATIONALLICENCE)springer-10.1007/s00023-010-0069-9 Inverse Scattering at Fixed Energy in de Sitter-Reissner-Nordström Black Holes [Elektronische Daten] [Thierry Daudé, François Nicoleau] 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(λ) at a fixed energy λ ≠ 0. More precisely, we consider the partial wave scattering matrices S(λ, n) (here λ ≠ 0 is the fixed energy and $${n \in \mathbb{N}^{*}}$$ 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 Λ of a dS-RN black hole (and thus its metric) can be uniquely determined from the knowledge of either the transmission coefficients T(λ, n), or the reflexion coefficients R(λ, n) (resp. L(λ, n)), for all $${n \in {\mathcal{L}}}$$ where $${\mathcal{L}}$$ is a subset of $${\mathbb{N}^{*}}$$ 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(λ, 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 $${\{z \in \mathbb{C}, Re(z) > 0 \}}$$ for which we have analytic uniqueness theorems at our disposal. Eventually, as a by-product of our method, we obtain reconstruction 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. Springer Basel AG, 2010 Daudé Thierry Department of Mathematics and Statistics, McGill University, 805 Sherbrooke South West, H3A 2K6, Montréal, QC, Canada aut Nicoleau François Laboratoire Jean Leray, UMR 6629, Université de Nantes, 2, rue de la Houssinière, BP 92208, 44322, Nantes Cedex 03, France aut Annales Henri Poincaré SP Birkhäuser Verlag Basel 12/1(2011-02-01), 1-47 1424-0637 12:1<1 2011 12 23 https://doi.org/10.1007/s00023-010-0069-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00023-010-0069-9 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Daudé Thierry Department of Mathematics and Statistics, McGill University, 805 Sherbrooke South West, H3A 2K6, Montréal, QC, Canada aut NATIONALLICENCE 700 1- Nicoleau François Laboratoire Jean Leray, UMR 6629, Université de Nantes, 2, rue de la Houssinière, BP 92208, 44322, Nantes Cedex 03, France aut NATIONALLICENCE 773 0- Annales Henri Poincaré SP Birkhäuser Verlag Basel 12/1(2011-02-01), 1-47 1424-0637 12:1<1 2011 12 23 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer