发表机构
Guangzhou City University of Technology; School of Electronic Information（广州城市理工学院; 电子信息学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究在正则系综框架下分析量子Oppenheimer-Snyder黑洞外部的热力学，发现近极端与大黑洞分支的鞍点结构，并在特定视界尺度处出现戴维斯型局部稳定性转变，澄清了已知结果的适用域。
AI 中文摘要
我们研究了先前从圈量子宇宙学中获得的量子Oppenheimer-Snyder（qOS）黑洞外部的局部正则热力学。时空取自文献；本文不声称提出新的黑洞解、正则延拓或奇点消解机制。在固定量子参数$\alpha$下，我们将外视界重写为无量纲形式，并获得了质量、霍金温度、熵和热容的精确表达式。这些表达式再现了早期分析中报道的对数熵项和热容发散。然后，我们将这些结果置于一个明确的、正则化的正则系综框架中。离壳正则作用量在近极端分支上有一个局部最小值，其热容为正；在大黑洞分支上有一个局部最大值，其热容为负。两个鞍点在$r_h/\sqrt{\alpha}=\sqrt{(4+2\sqrt{7})/3}$处合并，此时温度达到最大值且热容发散。由于渐近平坦配分函数在没有边界数据的情况下不可归一化，该发散被解释为戴维斯型局部稳定性转变，而非其本身作为全局一级相变。因此，本工作的主要贡献是对已知qOS热力学结果的透明正则鞍点组织，并精确陈述其适用范围和局限性。
英文摘要
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 $r_h/\sqrtα=\sqrt{(4+2\sqrt{7})/3}$, 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.
