Exponential energy decay for Kerr-de Sitter black holes beyond event horizons

TL;DR

This paper proves that linear waves decay exponentially over time in the spacetime of slowly rotating Kerr-de Sitter black holes, extending understanding of wave behavior in such curved backgrounds.

Contribution

It introduces a novel combination of resolvent estimates, red-shift effect, and parametrix construction to establish exponential decay beyond event horizons.

Findings

Exponential decay of linear waves on Kerr-de Sitter black holes.

Decay estimate valid beyond event horizons.

Method combines resolvent estimates with geometric effects.

Abstract

We establish an exponential decay estimate for linear waves on the Kerr-de Sitter slowly rotating black hole. Combining the cutoff resolvent estimate of arXiv:1003.6128 with the red-shift effect and a parametrix near the event horizons, we obtain exponential decay on the whole space.