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Kerr Black Hole Uniqueness
Abstract
We prove the black hole uniqueness conjecture in the axially symmetric, stationary vacuum setting: there is no regular, asymptotically flat equilibrium configuration with more than one horizon component. More precisely, we establish that in every such multi-horizon configuration, the logarithmic angle defect along every bounded axis rod is negative, which implies that the net interaction force across each such segment is attractive. The proof is based on a refined asymptotic analysis of the associated singular harmonic maps, partially drawn from the companion work [16], together with a global maximum principle bound for the Weyl conformal factor arising from a novel scalar curvature related differential inequality.
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BibTeX
@misc{han2026kerr,
title = {{Kerr Black Hole Uniqueness}},
author = {Qing Han and Marcus Khuri and Gilbert Weinstein and Jingang Xiong},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.23325},
eprint = {2608.23325},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.23325},
}
RIS
TY - UNPB
TI - Kerr Black Hole Uniqueness
AU - Qing Han
AU - Marcus Khuri
AU - Gilbert Weinstein
AU - Jingang Xiong
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2608.23325
UR - https://arxiv.org/abs/2608.23325
AB - We prove the black hole uniqueness conjecture in the axially symmetric, stationary vacuum setting: there is no regular, asymptotically flat equilibrium configuration with more than one horizon component. More precisely, we establish that in every such multi-horizon configuration, the logarithmic angle defect along every bounded axis rod is negative, which implies that the net interaction force across each such segment is attractive. The proof is based on a refined asymptotic analysis of the associated singular harmonic maps, partially drawn from the companion work [16], together with a global maximum principle bound for the Weyl conformal factor arising from a novel scalar curvature related differential inequality.
ER -