• Accepted Paper

Entropy dynamics in gravitational collapse: From Minkowski breaking to de Sitter thermodynamics

Francisco S. N. Lobo and Manuel E. Rodrigues

Phys. Rev. D - Accepted 15 October, 2026

DOI: https://doi.org/10.1103/ymsg-hcgp

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 $S_{\rm inner}=\pi h_c^2$ whose formal contribution decreases as the core shrinks; the n=0 Minkowski breaking obstructs a regular continuation within the ansatz. In Volovik’s framework, the signed entropy assignment for a homogeneous de Sitter Hubble volume 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 (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 might involve a quantum mechanism that remains speculative. Nevertheless, both frameworks embody the same thermodynamic principle, interior shrinkage changes the assigned entropy, with total entropy increase requiring an appropriate physical balance, 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 compatibility with the generalized second law is conditional on the entropy prescription and a justified environmental contribution.

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