Teukolsky on slowly-rotating Kerr-de Sitter in the vanishing $\Lambda$ limit

TL;DR

This paper establishes uniform energy and decay estimates for solutions to the Teukolsky equation on slowly-rotating Kerr-de Sitter spacetimes, valid as the cosmological constant approaches zero, extending previous results to a broader setting.

Contribution

It provides the first uniform estimates for Teukolsky solutions on Kerr-de Sitter backgrounds as $ ext{Lambda} o 0$, covering the entire exterior domain.

Findings

Uniform energy and Morawetz estimates for Teukolsky solutions

Extension of estimates up to $r o ext{Lambda}^{-1/2}$

Recovery of Kerr estimates in the $ ext{Lambda} o 0$ limit

Abstract

We prove energy, Morawetz and $r^p$-weighted estimates for solutions to the Teukolsky equation set on a slowly-rotating Kerr-de Sitter background. The main feature of our estimates is their uniformity with respect to the cosmological constant $\Lambda>0$ (thus allowed to tend to $0$), while they hold on the whole domain of outer communications, extending up to $r\sim \Lambda^{-\frac{1}{2}}$. As an application of our result, we recover well-known corresponding estimates for solutions to Teukolsky on a slowly-rotating Kerr background in the limit $\Lambda\to 0$.