A note on the quantization of angular momentum for black holes
Abstract
We argue that the gravitational path integral for rotating black holes is periodic in the angular velocity, implying the quantization of angular momentum in arbitrary dimensions for either asymptotically flat or AdS boundary conditions. In AdS3, this periodicity is a consequence of the boundary mapping class group. In higher dimensions, the periodicity arises from an infinite family of saddles labeled by integer shifts of the angular velocity unrelated to the boundary mapping class group; summing over these saddles enforces quantization independently of any large boundary diffeomorphism. We construct these saddles explicitly for Kerr-Newman black holes in both asymptotically flat space and AdS4, and observe that even the path integral for the 4D Schwarzschild black hole, typically the simplest case, receives contributions from an infinite set of rotating saddles.
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BibTeX
@misc{goker2026note,
title = {{A note on the quantization of angular momentum for black holes}},
author = {Jon Goker and Luca V. Iliesiu and Elisa Tabor},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.13774},
eprint = {2606.13774},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.13774},
}
RIS
TY - UNPB
TI - A note on the quantization of angular momentum for black holes
AU - Jon Goker
AU - Luca V. Iliesiu
AU - Elisa Tabor
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2606.13774
UR - https://arxiv.org/abs/2606.13774
AB - We argue that the gravitational path integral for rotating black holes is periodic in the angular velocity, implying the quantization of angular momentum in arbitrary dimensions for either asymptotically flat or AdS boundary conditions. In AdS_3, this periodicity is a consequence of the boundary mapping class group. In higher dimensions, the periodicity arises from an infinite family of saddles labeled by integer shifts of the angular velocity unrelated to the boundary mapping class group; summing over these saddles enforces quantization independently of any large boundary diffeomorphism. We construct these saddles explicitly for Kerr-Newman black holes in both asymptotically flat space and AdS_4, and observe that even the path integral for the 4D Schwarzschild black hole, typically the simplest case, receives contributions from an infinite set of rotating saddles.
ER -