Physics – Mathematical Physics
Scientific paper
2010-04-09
Rev.Math.Phys.22:431-484,2010; Annales Henri Poincare 12:1-47,2011
Physics
Mathematical Physics
40 pages
Scientific paper
10.1142/S0129055X10004004 10.100
In this paper, we consider massless Dirac fields propagating in the outer region of de Sitter-Reissner-Nordstr\"om 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 M\"untz 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.
Daude Thierry
Nicoleau François
No associations
LandOfFree
Inverse scattering at fixed energy in de Sitter-Reissner-Nordström black holes does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Inverse scattering at fixed energy in de Sitter-Reissner-Nordström black holes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Inverse scattering at fixed energy in de Sitter-Reissner-Nordström black holes will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-220616