Scattering Theory for the Charged Klein-Gordon Equation in the Exterior De Sitter-Reissner-Nordstr\"om Spacetime

TL;DR

This paper establishes asymptotic completeness for the charged Klein-Gordon equation in a specific black hole spacetime, interpreting scattering through null geodesics in an extended geometric framework.

Contribution

It proves asymptotic completeness for the charged Klein-Gordon equation in De Sitter-Reissner-Nordstr"om spacetime under small charge conditions and introduces a geometric interpretation of scattering.

Findings

Proves asymptotic completeness for small charge products.

Interprets scattering as transport along null geodesics.

Uses Kaluza-Klein extension for geometric analysis.

Abstract

We show asymptotic completeness for the charged Klein-Gordon equation in the exterior De Sitter-Reissner-Nordstr\"om spacetime when the product of the charge of the black hole with the charge of Klein-Gordon field is small enough. We then interpret scattering as asymptotic transports along principal null geodesics in a Kaluza-Klein extension of the original spacetime.