Nonlinear Stability of the Slowly-Rotating Kerr-de Sitter Family

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 (Hintz and Vasy, Acta Mathematica 220(1):1–206, 2018). Using the linear theory developed in the companion paper (Fang in Linear stability of the slowly-rotating Kerr-de Sitter family, 2022, https://doi.org/10.1007/s40818-025-00226-y ), 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 the initial data to be small only in the $$H^6$$ norm.