The Juhász Model 3.0: Unified Scale‑Field Dynamics, Stability Window, and the Black Hole Regime
Zoltán Juhász
Abstract
This work presents Version 3.0 of the Juhász Model, completing the unified scale–field framework introduced in Versions 1.0 and 2.0. In this theory, all physical structure, dynamics, and spacetime behavior emerge from a single scalar scale field ϕ(t,x), which encodes the slow contraction of matter itself while local physics remains invariant. Temporal evolution of the scale–field reproduces cosmological redshift and late‑time acceleration (Version 2.0), whereas spatial gradients generate effective gravitational potentials and local dynamical phenomena (Version 3.0). Version 3.0 introduces two key concepts: (1) the stability window, a regime in which the scale–field supports long‑lived bound structures without invoking dark matter, and (2) the dissolution regime, where the field becomes steep enough to erase stable matter configurations. This dissolution regime provides a physical interpretation of black hole interiors: instead of containing mass, they represent regions where the scale–field exits the stability window and matter loses its ability to exist in stable form. The paper develops the mathematical formulation of the unified dynamics, derives the conditions for stability and collapse, and explores the physical and cosmological implications of the scale–field. The resulting framework offers a coherent alternative to metric expansion, dark matter, and dark energy, replacing them with a single geometric degree of freedom. This work is part of a three‑paper series: – Version 1.0 (conceptual foundation + mechanical analogue): DOI: 10.5281/zenodo.20285489 – Version 2.0 (cosmological dynamics, Freimann extension): DOI: 10.5281/zenodo.20256495 – Version 3.0 (unified scale–field dynamics and black hole regime — this paper) Together, these works form the complete theoretical structure of the Juhász Model.