Black Holes as Thermodynamic Valves: A Discrete Hierarchical Bookkeeping Construction
Year: 2026
Type: article
Abstract: A discrete hierarchical bookkeeping map is defined that treats the black-hole interior as a thermodynamic valve. The map absorbs mass across a horizon only when an outer pressure meets a threshold proportional to the instantaneous core surface area, processes the absorbed mass at a rate proportional to that same area, and uses a single overall constant calibrated so that the time-averaged processing rate tracks the Hawking luminosity. With that one calibration the identical rules reproduce the standard Hawking scalings L∝M−2L \propto M^{-2}L∝M−2, τ∝M3\tau \propto M^{3}τ∝M3, T∝M−1T \propto M^{-1}T∝M−1 from 1 M⊙1\,M_\odot1M⊙ to 1011 M⊙10^{11}\,M_\odot1011M⊙. Mass is conserved and the exterior thermodynamics remain those of the outer horizon. Continuous bookkeeping runs from the horizon to a finite Smalling core; hierarchical continuum and spacetime tension supply the interior language. The core radius is an infrared input of the present construction. A 3+1 or consistent spherical evolution with hierarchical stress-energy that selects the core length as an output would test the candidate handshake between classical exterior general relativity and the interior processing scale. Not a solution of the Einstein equations. Not a quantum-gravity derivation. Not a detection claim.
Author: Smalling, Scott
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225812075
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