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Nonlinear stability of the slowly-rotating Kerr-de Sitter family
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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.
Forward citations
Cited by 3 Pith papers
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Linear stability of Kerr black holes in the full subextremal range
Proof that linearized perturbations of subextremal Kerr black holes decay to a linearized Kerr solution for the full range |a| < m.
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On the uniqueness of Kerr-de Sitter spacetimes
Under compatibility conditions on both horizons, every smooth stationary vacuum solution with positive cosmological constant is claimed to be isometric to Kerr-de Sitter in its stationary region.
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Teukolsky on slowly-rotating Kerr-de Sitter in the vanishing $\Lambda$ limit
Energy, Morawetz and r^p-weighted estimates are proved for Teukolsky equations on slowly-rotating Kerr-de Sitter, uniformly as the cosmological constant tends to zero, recovering known Kerr-Teukolsky estimates in the limit.
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