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arXiv · 2509.05789

On the uniqueness of Kerr-de Sitter spacetimes

Allen Juntao Fang
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Abstract

In this paper, we prove a series of results concerning the uniqueness of Kerr-de Sitter as a family of smooth stationary black hole solutions to the nonlinear Einstein vacuum equations with positive cosmological constant $\Lambda$. The results only assume smoothness rather than analyticity of the solution in question. The results use a two-sided approach to rigidity, requiring assumptions on both the event horizon and the cosmological horizon (or a neighborhood thereof) to formulate an appropriate unique continuation argument to prove the rigidity of Kerr-de Sitter.

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Allen Juntao Fang. 2025-09-06. On the uniqueness of Kerr-de Sitter spacetimes. https://arxiv.org/abs/2509.05789

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