At Most One Inner Killing Horizon in Stationary Black Holes
Abstract
Stationary-axisymmetric black holes are the standard theoretical framework for astrophysical black holes, yet their interiors remain largely inaccessible: the absence of a hypersurface-orthogonal timelike Killing vector renders the metric non-diagonal, and frame dragging obstructs the usual techniques for probing the interior. We prove that any stationary-axisymmetric black hole satisfying the classical energy conditions contains at most one nondegenerate inner Killing horizon per connected interior branch, irrespective of its matter content. For compact horizon sections, we apply the Raychaudhuri equation to the congruence normal to constant-time hypersurfaces: the strong energy condition makes the squared lapse subharmonic, and the maximum principle excludes a second inner horizon. For noncompact planar and hyperbolic sections central to holography, the null energy condition instead yields a monotonicity obstruction through a geometric flow we introduce here, the ``inverse lapse flow,'' whose weak continuation via viscosity solutions we also construct. The attractive nature of gravity, encoded in these energy conditions, thus both drives horizon formation and caps the number of inner horizons, revealing a striking dual role of the same focusing mechanism.
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BibTeX
@misc{ye2026most,
title = {{At Most One Inner Killing Horizon in Stationary Black Holes}},
author = {Jing-Peng Ye and Yu-Xuan Li and Run-Qiu Yang and Li Li},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.16698},
eprint = {2609.16698},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.16698},
}
RIS
TY - UNPB
TI - At Most One Inner Killing Horizon in Stationary Black Holes
AU - Jing-Peng Ye
AU - Yu-Xuan Li
AU - Run-Qiu Yang
AU - Li Li
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.16698
UR - https://arxiv.org/abs/2609.16698
AB - Stationary-axisymmetric black holes are the standard theoretical framework for astrophysical black holes, yet their interiors remain largely inaccessible: the absence of a hypersurface-orthogonal timelike Killing vector renders the metric non-diagonal, and frame dragging obstructs the usual techniques for probing the interior. We prove that any stationary-axisymmetric black hole satisfying the classical energy conditions contains at most one nondegenerate inner Killing horizon per connected interior branch, irrespective of its matter content. For compact horizon sections, we apply the Raychaudhuri equation to the congruence normal to constant-time hypersurfaces: the strong energy condition makes the squared lapse subharmonic, and the maximum principle excludes a second inner horizon. For noncompact planar and hyperbolic sections central to holography, the null energy condition instead yields a monotonicity obstruction through a geometric flow we introduce here, the ``inverse lapse flow,'' whose weak continuation via viscosity solutions we also construct. The attractive nature of gravity, encoded in these energy conditions, thus both drives horizon formation and caps the number of inner horizons, revealing a striking dual role of the same focusing mechanism.
ER -