2026/07/27 by Francisco S. N. Lobo, Manuel E. Rodrigues
#gr-qc #astro-ph.HE #hep-th
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=πhc2 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= sgn(H) π/H2 = 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.