Saddle-Order Universality in Ensemble-Averaged Black Hole Thermodynamics
Abstract
We establish a saddle-order proposition for the ensemble-averaged generalized free energy in reduced Euclidean black hole ensembles. Under regularity and stability assumptions, the leading fluctuation contribution is determined by the order of the first stabilizing term around the dominant saddle. An ordinary critical point is governed by a quartic soft mode, giving a quarter-temperature contribution instead of the familiar half-temperature Gaussian result. We verify this analytically for four-dimensional RN-AdS and Kerr-AdS black holes and map their thermodynamic controls to a common quartic normal form, whose scaling function connects the critical and Gaussian regimes along the zero-field one-well direction. The proposition also extends to coupled collective modes with weighted-homogeneous leading potentials. These results provide a unified description of reduced-ensemble fluctuations through black hole criticality.
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BibTeX
@misc{anand2026saddleorder,
title = {{Saddle-Order Universality in Ensemble-Averaged Black Hole Thermodynamics}},
author = {Ankit Anand and Peng Cheng},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.24344},
eprint = {2609.24344},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.24344},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Saddle-Order Universality in Ensemble-Averaged Black Hole Thermodynamics
AU - Ankit Anand
AU - Peng Cheng
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.24344
UR - https://arxiv.org/abs/2609.24344
AB - We establish a saddle-order proposition for the ensemble-averaged generalized free energy in reduced Euclidean black hole ensembles. Under regularity and stability assumptions, the leading fluctuation contribution is determined by the order of the first stabilizing term around the dominant saddle. An ordinary critical point is governed by a quartic soft mode, giving a quarter-temperature contribution instead of the familiar half-temperature Gaussian result. We verify this analytically for four-dimensional RN-AdS and Kerr-AdS black holes and map their thermodynamic controls to a common quartic normal form, whose scaling function connects the critical and Gaussian regimes along the zero-field one-well direction. The proposition also extends to coupled collective modes with weighted-homogeneous leading potentials. These results provide a unified description of reduced-ensemble fluctuations through black hole criticality.
ER -