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<p>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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\Lambda &gt; 0\)</EquationSource> </InlineEquation>, 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, <a href="https://doi.org/10.1007/s40818-025-00226-y">https://doi.org/10.1007/s40818-025-00226-y</a>), 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 <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(H^6\)</EquationSource> </InlineEquation> norm.</p>

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

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  • 发表日期：

    2026年2月3日

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  • Allen Juntao Fang

摘要

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.