Planck-Ion Feedback Loop and Singularity Resolution: A Formal Unified Theory of Super-Heavy Element Phase Transitions in Black Hole Cores Ver1

Planck-Ion Feedback Loop and Singularity Resolution: A Formal Theory of Super-Heavy Element Phase Transitions in Black Hole Cores Sungmin Lee Independent Researcher [email protected] December 14, 2025 Abstract We present a non-singular framework for black hole interiors by integrating General Relativity with a hierarchical nuclear phase transition model. This work, building upon the theoretical and operational foundations established in previous iterations (Ver.13/14), rejects the "singleelement core" assumption and proposes a core composed of a lattice of physical super-heavy elements (SHE). As gravitational collapse proceeds, the reduction in the number of nuclei drives the core radius toward a finite limit Rmin. We formalize the Planck-Ion Feedback Loop: curvature-induced tidal forces trigger the ionization of SHEs, creating a lossless plasma buffer that provides quantum-mechanical repulsive pressure. This state reaches unitary equilibrium at the Planck scale, suggesting new pathways for gravitational wave phenomenology. 1 Introduction The gravitational singularity at r= 0 remains the most significant challenge in classical General Relativity. Traditional models often assume a vacuum interior or an unphysical point mass. In this work, we extend the integrated theory of curvature-quantum interactions introduced in the author’s prior framework (Ver.13/14), proposing that the black hole interior is a high-energy environment where nuclear physics and geometry are inextricably coupled. Instead of a single-step collapse, we model the transition from neutron-degenerate matter to a structured core of super-heavy elements (SHE). Core stabilization is achieved through a dynamic Planck-Ion Feedback Loop, where curvature energy is converted into plasma pressure, preventing unphysical divergence while preserving general relativistic consistency. 1 2 Sequential Nucleosynthesis and the SHE Core 2.1 From Neutron Matter to Hierarchical Lattice As the density surpasses nuclear saturation, nucleons undergo sequential fusion into the heaviest physically permissible elements. This hierarchical SHE lattice respects the conservation of baryon number while reducing the total number of independent particles N. The macroscopic radius R contracts as a function of the fusion rate: dR dNfusion ∝1 ρ(N, K)(1) where Kis the Kretschmann scalar. This process continues until the core reaches a "Super-Heavy Element Star" configuration near Rmin. 3 The Planck-Ion Feedback Mechanism 3.1 Tidal Ionization Trigger Micro-anisotropies σare amplified by the extreme curvature near the core boundary. The tidal potential gradient ∆Φ across a SHE nucleus of radius rnis given by: ∆Φ ≈1 2√Kr2 nc2σ(2) When the energy e∆Φ exceeds the k-shell binding energy E(k) b, high-order ionization occurs. 3.2 Self-Regulating Dynamics The system enters a recursive cycle of stabilization: 1. Lossless Plasma Activation: Ionization creates a high-density plasma buffer. Due to the trapped surface geometry, this energy provides a direct counter-pressure Pplasma against gravity. 2. Gravitational Attenuation: The plasma pressure halts the inflow, leading to "Higher-Order Ion" states. 3. Recursive Contraction: Metric work consumes plasma energy, causing micro-contraction and re-triggering ionization at higher energy levels. 4 Planck-Scale Decomposition At the limit of this feedback loop, the combined effects of extreme density ρ→ρPand quantum instability trigger the decomposition of matter into Planck-scale constituents. The core reaches 2 Unitary Equilibrium, maintained at Planck-interval separations lP: ∆x≈rℏG c3, ρcore ≈c5 ℏG2(3) This is a dynamic equilibrium sustained by curvature energy and quantum fluctuations. 5 Core Instability and Gravitational Waves The internal energy flow within the SHE plasma core is subject to quantum fluctuations. If the energy Eint becomes unstable through non-linear coupling between Kand the scalar field Ψ, metric perturbations hµν may propagate outward. Detection of high-frequency GW background or postmerger "echoes" could serve as evidence for this structured, non-singular core. 6 Conclusion This framework replaces the mathematical void of a singularity with a physically grounded SHEplasma core. By formalizing the Planck-Ion Feedback Loop, we show that collapse is halted by the very curvature that drives it. The core exists in a state of unitary equilibrium, bridging the gap between General Relativity and Quantum Mechanics. Project Resources and Previous Versions The present study is the latest formal evolution of the theory. For reference to the earlier development stages and the foundational source code, please see the following records: •Current Study (Preprint/Ver.14 Results): https://doi.org/10.5281/zenodo.17608173 •Foundational Source Code (Ver.13): https://doi.org/10.5281/zenodo.17592707 Author Contributions The author conducted all theoretical derivations independently. This work is based on the author’s proprietary model. AI tools were utilized for LaTeX typesetting and linguistic refinement under the author’s strict supervision. License This work is provided under the Creative Commons Attribution 4.0 International (CC BY 4.0) License. 3 References [1] Lee, S., Planck-Ion Feedback in Finite-Radius Black Holes (Ver.13/14), Zenodo, 2025. [2] Misner, C. W., et al., Gravitation, 1973. [3] Oganessian, Y. T., Super-heavy elements, Rep. Prog. Phys, 2015. [4] Rovelli, C., Planck Stars, Int. J. Mod. Phys. D, 2014. 4