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This theoretical study examines black hole entropy through two complementary frameworks: the OCK construction involving Schwarzschild black holes with de Sitter cores, and Volovik's local thermodynamics of de Sitter vacuum. The research demonstrates that both frameworks support the same thermodynamic principle where shrinking interiors drive systems toward increased total entropy, with the OCK parameter's integer nature suggesting a quantized entropy spectrum. The analysis reveals that expanding de Sitter space carries positive entropy while contracting de Sitter space carries negative entropy, with both scenarios satisfying the generalized second law of thermodynamics.
Why it matters
This work advances our theoretical understanding of one of physics' fundamental mysteries—the origin of black hole entropy—and suggests a potential statistical interpretation through quantized entropy spectra. The findings could influence future developments in quantum gravity theory and our comprehension of extreme gravitational phenomena.
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arXiv:2607.24349v1 Announce Type: cross
Abstract: 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 $S_{rm inner}=pi h_c^2$ 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 $S_{rm dS}= operatorname{sgn}(H),pi/H^{2} = operatorname{sgn}(H),A/4$: expanding de Sitter ($H>0$) carries positive entropy, while contracting de Sitter ($H2$; 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.
Source: Entropy dynamics in gravitational collapse: From Minkowski breaking to de Sitter thermodynamics