Nonlinear stability of the slowly-rotating Kerr-de Sitter family

TL;DR

This paper offers a new proof demonstrating the nonlinear stability of slowly-rotating Kerr-de Sitter black holes, simplifying previous methods and requiring only small initial data in the $H^6$ norm.

Contribution

It provides a streamlined proof of nonlinear stability for Kerr-de Sitter black holes, avoiding Nash-Moser techniques and leveraging linear theory.

Findings

Nonlinear stability of Kerr-de Sitter established

Proof avoids Nash-Moser iteration

Initial data smallness in $H^6$ norm suffices

Abstract

In this paper, we provide a new proof of nonlinear stability of the slowly-rotating Kerr-de Sitter family of black holes as a family of solutions to the Einstein vacuum equations with cosmological constant $\Lambda>0$, originally established by Hintz and Vasy in their seminal work [arXiv:1606.04014]. Using the linear theory developed in an upcoming companion paper, we prove the nonlinear stability of slowly-rotating Kerr-de Sitter using a bootstrap argument, avoiding the need for a Nash-Moser argument, and requiring initial data small only in the $H^6$ norm.