Inverse scattering in de Sitter-Reissner-Nordstr\"om black hole spacetimes

TL;DR

This paper investigates how to uniquely determine the mass, charge, and cosmological constant of a de Sitter-Reissner-Nordström black hole using inverse scattering methods applied to massive charged Dirac fields, providing explicit asymptotic expansions and conditions for parameter recovery.

Contribution

It introduces a precise high-energy asymptotic expansion of the scattering matrix and demonstrates unique parameter recovery from reflection coefficients in de Sitter-Reissner-Nordström black holes.

Findings

High-energy asymptotic expansion of the scattering matrix obtained.

Unique recovery of black hole parameters from scattering data established.

Reflection coefficients determine parameters in the presence of a cosmological constant.

Abstract

In this paper, we study the inverse scattering of massive charged Dirac fields in the exterior region of (de Sitter)-Reissner-Nordstr\"om black holes. First 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 allows to recover uniquely the mass, the charge and the cosmological constant of the black hole. Second, 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.