# 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.

## Key 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.

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Source: https://tomesphere.com/paper/1812.09390