Canonical-Ensemble Stability of the Quantum Oppenheimer-Snyder Black-Hole Exterior
Abstract
We study the local canonical thermodynamics of the quantum Oppenheimer--Snyder (qOS) black-hole exterior previously obtained from loop quantum cosmology. The spacetime is adopted from the literature; no new black-hole solution, regular extension, or singularity-resolution mechanism is claimed here. At fixed quantum parameter α, we rewrite the outer horizon in a dimensionless form and obtain exact expressions for the mass, Hawking temperature, entropy, and heat capacity. These expressions reproduce the logarithmic entropy term and the heat-capacity divergence reported in earlier analyses. We then place those results in an explicit, regulated canonical-ensemble framework. The off-shell canonical action has a local minimum on a near-extremal branch with positive heat capacity and a local maximum on a large-black-hole branch with negative heat capacity. The two saddles merge at rh/√α=√((4+2√7)/3), where the temperature is maximal and the heat capacity diverges. Because the asymptotically flat partition function is not normalizable without boundary data, this divergence is interpreted as a Davies-type local stability transition, not by itself as a global first-order phase transition. The principal contribution of this work is therefore a transparent canonical-saddle organization of known qOS thermodynamic results, together with a precise statement of its domain and limitations.
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BibTeX
@misc{chen2026canonicalensemble,
title = {{Canonical-Ensemble Stability of the Quantum Oppenheimer-Snyder Black-Hole Exterior}},
author = {Wen-Xiang Chen},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.13865},
eprint = {2609.13865},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.13865},
}
RIS
TY - UNPB
TI - Canonical-Ensemble Stability of the Quantum Oppenheimer-Snyder Black-Hole Exterior
AU - Wen-Xiang Chen
PY - 2026
DA - 2026/09/12
PB - arXiv
DO - 10.48550/arxiv.2609.13865
UR - https://arxiv.org/abs/2609.13865
AB - We study the local canonical thermodynamics of the quantum Oppenheimer--Snyder (qOS) black-hole exterior previously obtained from loop quantum cosmology. The spacetime is adopted from the literature; no new black-hole solution, regular extension, or singularity-resolution mechanism is claimed here. At fixed quantum parameter α, we rewrite the outer horizon in a dimensionless form and obtain exact expressions for the mass, Hawking temperature, entropy, and heat capacity. These expressions reproduce the logarithmic entropy term and the heat-capacity divergence reported in earlier analyses. We then place those results in an explicit, regulated canonical-ensemble framework. The off-shell canonical action has a local minimum on a near-extremal branch with positive heat capacity and a local maximum on a large-black-hole branch with negative heat capacity. The two saddles merge at r_h/√α=√((4+2√7)/3), where the temperature is maximal and the heat capacity diverges. Because the asymptotically flat partition function is not normalizable without boundary data, this divergence is interpreted as a Davies-type local stability transition, not by itself as a global first-order phase transition. The principal contribution of this work is therefore a transparent canonical-saddle organization of known qOS thermodynamic results, together with a precise statement of its domain and limitations.
ER -