AI 中文总结
研究黑洞熵起源，结合OCK构造与德西特真空局部热力学，通过哈勃参数符号连接两者，揭示引力坍缩中熵流图景，暗示量子化熵谱与黑洞熵统计解释，广义第二定律在相关框架成立。
AI 中文摘要
黑洞熵的起源仍是现代物理学中最深奥的谜团之一。近期两项进展为此谜题提供了互补观点：具有德西特核心的正则史瓦西黑洞的熵释放（OCK构造），以及德西特真空的局部热力学（沃洛维克）。在OCK框架中，内视界携带正的贝肯斯坦 - 霍金熵$S_{\rm inner}=\pi h_c^2$，随着核心收缩逐渐释放，直到经典闵可夫斯基破缺在$n = 0$时阻碍演化。在沃洛维克框架中，均匀德西特区域的总熵为$S_{\rm dS}= \operatorname{sgn}(H)\,\pi/H^{2} = \operatorname{sgn}(H)\,A/4$。我们表明哈勃参数的符号是连接这两张图的统一元素。OCK核心仅在$n>2$时是德西特的；闵可夫斯基破缺是经典运动学阻碍，而非向收缩德西特相的动力学转变。任何膨胀和收缩区域之间的联系都需要一种仍具推测性的量子机制。不过，两个框架都体现了相同的热力学原理，内部收缩驱使系统总熵增加，共同提供了引力坍缩期间熵流的一致图景。OCK参数的整数性质暗示了量子化的熵谱和黑洞熵的统计解释，广义第二定律在两个框架中都成立，在推测的量子联系中若适当考虑环境熵也成立。
英文摘要
The origin of black hole entropy remains one of the deepest mysteries in modern physics. Two recent developments offer complementary perspectives on this puzzle: the entropy release from regular Schwarzschild black holes with a de Sitter core (the OCK construction), and the local thermodynamics of the de Sitter vacuum (Volovik). In the OCK framework, the inner horizon carries positive Bekenstein-Hawking entropy $S_{\rm inner}=πh_c^2$ that is gradually released as the core shrinks, until a classical Minkowski breaking obstructs the evolution at $n=0$. In Volovik's framework, the total entropy of a homogeneous de Sitter region is $S_{\rm dS}= \operatorname{sgn}(H)\,π/H^{2} = \operatorname{sgn}(H)\,A/4$: expanding de Sitter ($H>0$) carries positive entropy, while contracting de Sitter ($H<0$) carries negative entropy. We show that the sign of the Hubble parameter is the unifying element linking the two pictures. The OCK core is de~Sitter only for $n>2$; the Minkowski breaking is a classical kinematic obstruction, not a dynamical transition to a contracting de Sitter phase. Any connection between the expanding and contracting regimes would require a quantum mechanism that remains speculative. Nevertheless, both frameworks embody the same thermodynamic principle, the shrinking of the interior drives the system toward increased total entropy, and together they provide a consistent picture of entropy flow during gravitational collapse. The integer nature of the OCK parameter suggests a quantized entropy spectrum and a statistical interpretation of black hole entropy, while the generalized second law is satisfied in both frameworks, and in the speculated quantum connection provided the environmental entropy is properly accounted for.
Comments14 pages, 2 figures
