Conformal Scattering and the Goursat Problem for Dirac Fields in the Interior of Charged Spherically Symmetric Black Holes

TL;DR

This paper develops a conformal scattering framework for Dirac fields inside charged black holes, solving the characteristic Cauchy problem on horizons by transforming it into wave equations.

Contribution

It introduces a novel conformal scattering theory for Dirac fields in black hole interiors, addressing the characteristic Cauchy problem through wave equation systems.

Findings

Successfully constructs the scattering theory in the black hole interior.

Provides a method to solve the characteristic Cauchy problem on horizons.

Reinterprets wave equation solutions as Dirac field components.

Abstract

We construct a conformal scattering theory for Dirac fields in the interior of a Reissner-Nordstr\"om-like black hole, between the black hole event horizon and the Cauchy horizon. The main result is a resolution of the characteristic Cauchy problem for the Dirac equation on the horizons by solving a system of wave equations and re-interpreting its solution as the components of the required Dirac solution.