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

2021/12/14 by Fang, Allen Juntao · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2112.07183

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 Λ>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 H⁶ norm.

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• Future stability of solutions of the Einstein-nonlinear scalar field system with decelerated expansion
• Asymptotia of Kerr-de Sitter Black Holes

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