Spacelike Initial Data for Black Hole Stability

期刊论文
发表日期：

2025年9月1日

查看全文

Allen Juntao Fang,
Jérémie Szeftel,
Arthur Touati

摘要

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 $r^{-1}$ $r^{- 1}$ fall-off and the topology of $\mathbb {R}^3\setminus \{r<1\}$ $R^{3} \ {r < 1}$ 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).