Recovering the mass and the charge of a Reissner-Nordstr\"om black hole by an inverse scattering experiment

TL;DR

This paper develops an inverse scattering method to accurately determine the mass and charge of a Reissner-Nordström black hole by analyzing high-energy asymptotics of the scattering matrix for massless Dirac fields.

Contribution

It introduces a stationary inverse scattering approach to uniquely recover black hole parameters from scattering data, advancing methods in black hole characterization.

Findings

Successfully recovers black hole mass and charge from scattering data

Provides explicit high-energy asymptotic expansion of the scattering matrix

Establishes uniqueness of the inverse problem solution

Abstract

In this paper, we study inverse scattering of massless Dirac fields that propagate in the exterior region of a Reissner-Nordstr\"om black hole. Using a stationary approach we determine precisely the leading terms of the high-energy asymptotic expansion of the scattering matrix that, in turn, permit us to recover uniquely the mass of the black hole and its charge up to a sign.