Rigidity of stationary black holes with small ADM angular momentum
Abstract
We prove global rigidity of smooth asymptotically flat stationary vacuum black holes with sufficiently small ADM angular momentum, under global regularity, bifurcation, and maximal-hypersurface assumptions, with a threshold depending on fixed geometric bounds. This answers the question of Alexakis, Ionescu, and Klainerman concerning replacement of their smallness assumption on the stationary field at the bifurcation sphere by smallness of the angular momentum at infinity. The main step establishes Kerr rigidity near infinity for arbitrary angular momentum. We transform the vacuum metric into an Einstein--Maxwell family and compare null focusing at its limiting end with the area--charge inequality on compact maximal hypersurfaces, constructed by continuation through the family. Equality determines both the transformed metric and its stationary field, from which the inverse transformation recovers Kerr. Two Kerr identities then give the horizon estimate required for the global conclusion.
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BibTeX
@misc{radu2026rigidity,
title = {{Rigidity of stationary black holes with small ADM angular momentum}},
author = {Alexandru F. Radu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.09729},
eprint = {2610.09729},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.09729},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Rigidity of stationary black holes with small ADM angular momentum
AU - Alexandru F. Radu
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.09729
UR - https://arxiv.org/abs/2610.09729
AB - We prove global rigidity of smooth asymptotically flat stationary vacuum black holes with sufficiently small ADM angular momentum, under global regularity, bifurcation, and maximal-hypersurface assumptions, with a threshold depending on fixed geometric bounds. This answers the question of Alexakis, Ionescu, and Klainerman concerning replacement of their smallness assumption on the stationary field at the bifurcation sphere by smallness of the angular momentum at infinity. The main step establishes Kerr rigidity near infinity for arbitrary angular momentum. We transform the vacuum metric into an Einstein--Maxwell family and compare null focusing at its limiting end with the area--charge inequality on compact maximal hypersurfaces, constructed by continuation through the family. Equality determines both the transformed metric and its stationary field, from which the inverse transformation recovers Kerr. Two Kerr identities then give the horizon estimate required for the global conclusion.
ER -