Project: The Quantum Lenz’s Law (QLL) Series (Part 3 of 5) This report provides the formal mathematical proof of the QLL framework, demonstrating its consistency within the Semiclassical Einstein Field Equations. By identifying the Renormalized Stress-Energy Tensor as an "Induced Current," we prove that the vacuum must polarize to generate the negative energy flux required for black hole stability and mass loss. THE COMPLETE SERIES: Part 1: A Quantum Lenz's Law – The Fundamental Postulate. DOI: 10.5281/zenodo.17858086Part 2: Chronetic Rate – The temporal framework for induction. DOI: 10.5281/zenodo.18201750Part 3: The Semiclassical Master Equation – (This Report) The Formal Geometric Proof. DOI: 10.5281/zenodo.18212708Part 4: Primordial Quantum Lenz's Law – Application to the Cosmic Bounce. DOI: 10.5281/zenodo.18214970Part 5: B-Mode Polarization Signatures – Observational Evidence. DOI: 10.5281/zenodo.18218853 AUTHOR ORCID: 0009-0002-8135-0645 ABSTRACT: The Semiclassical Master Equation This paper presents a formal proof for a unified "Master Equation" in semiclassical gravity, grounded in the principle of Quantum Lenz's Law (QLL). By integrating the Renormalized Stress-Energy Tensor (RSET) into the Raychaudhuri equation, the work demonstrates that the quantum vacuum response to gravitational flux change acts as a regulatory "opposition." Utilizing the Generalized Uncertainty Principle (GUP), the proof shows that this Lenzian counter-pressure effectively violates the Null Energy Condition in high-curvature regimes, halting gravitational collapse at the Planck scale. The result is the replacement of classical singularities with stable Planck-scale remnants, providing a consistent mathematical framework for cosmological back-reaction and stability, analogous to Le Chatelier’s Principle in thermodynamics. This work serves as the technical foundation for the QLL series archived in the Zenodo Archive Collection.
Lee Holmes (Sun,) studied this question.