# Conformal Scattering of Maxwell Fields on Reissner-Nordstr{\o}m-de Sitter Black Hole Spacetimes

## TL;DR

This paper develops a comprehensive conformal scattering theory for Maxwell fields around Reissner-Nordström-de Sitter black holes, utilizing energy decay results to establish the properties of trace operators and solve the Goursat problem.

## Contribution

It introduces a complete conformal scattering framework for Maxwell fields on these black hole spacetimes, including the construction of trace operators and solving the characteristic Cauchy problem.

## Key findings

- Trace operators are injective with closed ranges.
- Trace operators are surjective.
- Established a full scattering theory for Maxwell fields on Reissner-Nordström-de Sitter spacetime.

## Abstract

We construct a complete conformal scattering theory for Maxwell fields in the static exterior region of a Reissner-Nordstr{\o}m-de Sitter black bole spacetime. This is done using uniform energy decay results that we obtain in a separate paper, to show that the trace operators are injective and have closed ranges. We then solve the Goursat problem (characteristic Cauchy problem) for Maxwell fields on the null boundaries showing that the trace operators are also surjective.