Decay of the Local Energy for the Charged Klein-Gordon Equation in the Exterior De Sitter-Reissner-Nordstr\"om Spacetime

TL;DR

This paper proves that solutions to the charged Klein-Gordon equation in the exterior De Sitter-Reissner-Nordström spacetime exhibit decay of local energy, using a resonance expansion approach to analyze the local propagator.

Contribution

It introduces a resonance expansion method to demonstrate local energy decay for the charged Klein-Gordon equation in this specific spacetime.

Findings

Decay of local energy established

Resonance expansion used for analysis

Method applicable to charged scalar fields in curved spacetime

Abstract

We show decay of the local energy of solutions of the charged Klein-Gordon equation in the exterior De Sitter-Reissner-Nordstr\"om spacetime by means of a resonance expansion of the local propagator.