Conformal Derivation of Regular Black Holes in Scalar-Tensor Gravity: The Hembrom Solution

This paper mathematically resolves one of the biggest breakdowns in General Relativity: the infinite singularity at the center of a black hole. It provides an exact, dynamically stable framework—the Hembrom Solution—that halts infinite gravitational collapse, replacing the singularity with a finite, regular spacetime core. How It Works (The 3 Pillars) The Advanced Geometry: Instead of allowing the gravitational force to blow up to infinity as distance (r) approaches zero, the paper introduces the "Advanced Hembrom Metric. " This uses a cubic regulator (H³) to create a physical buffer at the Planck scale. The Conformal Reconstruction: Many models fail because physicists try to guess the metric, the scalar field, and the energy potential all at once, which breaks the equations. This paper bypasses that trap. It maps the physical universe into a mathematically simpler space (the Einstein Frame), derives the exact potential required to hold the black hole open, and maps it back. There is no guesswork. The Mathematical Proof: The paper explicitly calculates the limits of the spacetime curvature (the Ricci scalar). It proves that the curvature does not go to infinity. Instead, it maxes out at a specific, finite mathematical limit: 20GMH³.