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arXiv · 2405.02071

Spacelike initial data for black hole stability

Allen Juntao Fang·Jérémie Szeftel·Arthur Touati
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Abstract

We construct initial data suitable for the Kerr stability conjecture, that is, solutions to the constraint equations on a spacelike hypersurface with boundary entering the black hole horizon that are arbitrarily decaying perturbations of a Kerr initial data set. This results from a more general perturbative construction on any asymptotically flat initial data set with the topology of $\mathbb{R}^3\setminus\{r<1\}$ enjoying some analyticity near and at the boundary. In particular, we design a suitable mixed boundary condition for the elliptic operator of the conformal method in order to exclude the Killing initial data sets (KIDS).

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Allen Juntao Fang, Jérémie Szeftel, Arthur Touati. 2024-05-03. Spacelike initial data for black hole stability. https://arxiv.org/abs/2405.02071

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