Conditional non-linear stability of Kerr-de Sitter spacetimes in the full subextremal range

TL;DR

This paper proves the conditional stability of Kerr-de Sitter black holes within the full subextremal range, assuming mode stability, by extending techniques used in slowly rotating cases and addressing key technical challenges.

Contribution

It extends the stability proof to the full subextremal range by implementing constraint damping and verifying technical conditions at the trapped set.

Findings

Stability of Kerr-de Sitter black holes in the full subextremal range

Implementation of constraint damping techniques

Verification of subprincipal symbol conditions at the trapped set

Abstract

We show the stability of Kerr-de Sitter black holes, in the full subextremal range, as solutions of the vacuum Einstein equation with a positive cosmological constant under the assumption that mode stability holds for these spacetimes. The method is similar to the (unconditional) proof in the slowly rotating case by Hintz and Vasy. The key novelties are the implementation of constraint damping in the full subextremal range as well as the verification of a subprincipal symbol condition at the trapped set.