A Mechanical Extension of General Relativity: The Singularity in Equilibrium

This work provides a mechanical resolution to the Black Hole Information Paradox by demonstrating that the Stiffness Matching Principle (SMP) halts singular collapse at a finite, stable equilibrium. By identifying the singularity as a physical state of mechanical saturation rather than a mathematical infinity, this model offers specific, testable predictions for Schwarzschild precession anomalies in stellar orbits near supermassive black holes. This paper proposes a foundational extension to General Relativity (GR) by addressing the structural limitations of the spacetime manifold at extreme energy densities. Building upon the mechanical derivation of the gravitational constant G as a dynamic ratio G = c² / (8π + Pₘ), we propose that the singularity results in a state of equilibrium. Rather than a mathematical point of infinite density, the singularity is identified as a physical state of mechanical saturation. We demonstrate that when localized field pressure Pₘ matches the intrinsic vacuum stiffness (8π), the manifold reaches a structural limit of compression, resulting in a stable state of equilibrium. This Saturated Equilibrium model proposes a resolution to the Black Hole Information Paradox by ensuring that quantum states are preserved within a finite, saturated volumetric structure, thereby maintaining quantum unitarity. The paper further provides observational pathways for verification, specifically predicting a "Precession Deficiency" in the Schwarzschild precession of the star S2 at Sagittarius A* via the modified relation: Δϕ_SMP = Δϕ_GR [ 8π / (8π + Pₘ) ]