Constrain the number of inner horizons from gravitational Noether charges
Abstract
A central question in the study of black hole interiors is how matter and geometry constrain the number of horizons. In Einstein gravity, one known method is to use the ADM decomposition of the field equations to derive a differential inequality for the lapse, which then constrains the possible multiple inner horizons. We show that the same obstruction can instead be formulated through the Komar integral as a bulk-boundary balance of gravitational Noether charge. In higher-curvature gravity, a direct ADM analysis becomes more complicated, whereas the gravitational Noether charge naturally retains this bulk-boundary structure. We naturally apply the gravitational Noether charge analysis to Lovelock gravity. We introduce a TCC-like curvature condition and prove that, together with the thermodynamically motivated assumption of positive Wald entropy, it allows at most one nondegenerate inner Killing horizon inside a nondegenerate event horizon. This suggests that the obstruction reflects a compatibility between bulk gravitational response and horizon thermodynamics.
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BibTeX
@misc{ye2026constrain,
title = {{Constrain the number of inner horizons from gravitational Noether charges}},
author = {Jing-Peng Ye and Run-Qiu Yang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.30812},
eprint = {2610.30812},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.30812},
}
RIS
TY - UNPB
TI - Constrain the number of inner horizons from gravitational Noether charges
AU - Jing-Peng Ye
AU - Run-Qiu Yang
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.30812
UR - https://arxiv.org/abs/2610.30812
AB - A central question in the study of black hole interiors is how matter and geometry constrain the number of horizons. In Einstein gravity, one known method is to use the ADM decomposition of the field equations to derive a differential inequality for the lapse, which then constrains the possible multiple inner horizons. We show that the same obstruction can instead be formulated through the Komar integral as a bulk-boundary balance of gravitational Noether charge. In higher-curvature gravity, a direct ADM analysis becomes more complicated, whereas the gravitational Noether charge naturally retains this bulk-boundary structure. We naturally apply the gravitational Noether charge analysis to Lovelock gravity. We introduce a TCC-like curvature condition and prove that, together with the thermodynamically motivated assumption of positive Wald entropy, it allows at most one nondegenerate inner Killing horizon inside a nondegenerate event horizon. This suggests that the obstruction reflects a compatibility between bulk gravitational response and horizon thermodynamics.
ER -