正则海沃德黑洞的精确解析相变、视界双稳性和热力学状态空间表示
Exact Analytical Phase Transitions, Horizon Bistability, and Thermodynamic State-Space Representation of Regular Hayward Black Holes
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中文总结 AI 辅助
该研究针对正则海沃德黑洞，通过评估相关物理量得出精确解析阈值与统一热力学状态空间表示，解决其相结构问题，发现视界双稳性、戴维斯奇点作用，还得到临界熵并引入诊断方法，为量子引力现象学提供定量框架。
中文摘要 AI 辅助
我们为正则海沃德黑洞建立了精确的解析阈值，并给出了统一的热力学状态空间表示，无需数值近似即可解决完整的相结构问题。通过相对于经典史瓦西基线评估霍金温度、亥姆霍兹自由能和热容量，我们得出了在\(r_h = \sqrt3l\)处零温度极值遗迹的精确几何分水岭，以及在\(r_h = 3l\)处的精确戴维斯临界转变。在中间区域\(\sqrt{3}l < r_h < 3l\)内，我们发现了一种独特的视界双稳性，其中两个不同的视界半径具有相同的自由能和温度分布。我们证明戴维斯奇点充当了精确的热力学分界线，将局部稳定（\(C_V > 0\)）的量子小黑洞分支与不稳定（\(C_V < 0\)）的大黑洞分支分开。此外，我们在临界转折点评估了精确的积分非面积定律熵，得到\(S_{turn} = \pi l^2 \left[ \frac{63}{8} + 2\ln(8l^2) \right]\)。最后，我们引入了一个紧凑的、三参数的热力学状态空间诊断方法，该方法跟踪正则黑洞从经典热蒸发到冷遗迹锁定的连续演化，为量子引力现象学提供了一个定量框架。
英文摘要
We establish exact analytical thresholds and present a unified thermodynamic state-space representation for the regular Hayward black hole, resolving the full phase structure without reliance on numerical approximations. By evaluating the Hawking temperature, Helmholtz free energy, and heat capacity against the classical Schwarzschild baseline, we derive the exact geometric watershed for the zero-temperature extremal remnant at $r_h = \sqrt3l$, along with the exact Davies critical transition at $r_h = 3l$. Within the intermediate regime $\sqrt{3}l < r_h < 3l$, we uncover a distinct horizon bistability where two distinct horizon radii share identical free energy and temperature profiles. We demonstrate that the Davies singularity acts as a precise thermodynamic divide, separating a locally stable ($C_V > 0$) quantum Small Black Hole branch from an unstable ($C_V < 0$) Large Black Hole branch. Furthermore, we evaluate the exact integrated non-area law entropy at the critical turning point, yielding $S_{turn} = πl^2 \left[ \frac{63}{8} + 2\ln(8l^2) \right]$. Finally, we introduce a compact, 3-parameter thermodynamic state-space diagnostic that tracks the continuous evolution of regular black holes from classical thermal evaporation to cold remnant lock, offering a quantitative framework for quantum-gravity phenomenology.
