INVERSE SCATTERING IN DE SITTER–REISSNER–NORDSTRÖM BLACK HOLE SPACETIMES

Abstract

In this paper, we study the inverse scattering of massive charged Dirac fields in the exterior region of (de Sitter)–Reissner–Nordström black holes. Firstly, we obtain a precise high-energy asymptotic expansion of the diagonal elements of the scattering matrix (i.e. of the transmission coefficients) and we show that the leading terms of this expansion allow to recover uniquely the mass, the charge and the cosmological constant of the black hole. Secondly, in the case of nonzero cosmological constant, we show that the knowledge of the reflection coefficients of the scattering matrix on any interval of energy also permits to recover uniquely these parameters.