Black Holes as Super-Stars: The Mechanical Resolution of Singularities, the Mass Gap, and the Information Paradox in the Quantum Gravity Theory (QGT)

This paper presents a comprehensive, mathematically rigorous framework for the Quantum Gravity Theory (QGT) applied to the extreme environments of black holes. We replace the abstract geometric curvature of General Relativity (GR) and its inevitable mathematical singularities with a physical, mechanical field dynamics governed by a single complex scalar field ψ. We postulate that a black hole is not a geometric hole in spacetime, but a super-dense, non-singular Super-Star composed of a macroscopic cluster of Q-balls. We provide exact derivations proving that the macroscopic Newtonian gravitational constant G emerges naturally from the microscopic self-interactions of the ψ field via spontaneous symmetry breaking and the Goldstone mechanism, bypassing the short-range Yukawa suppression. We derive the mechanical Tolman-Oppenheimer-Volkoff (TOV) equivalent for this Super-Star, demonstrating that the repulsive self-interaction term (+g|ψ|^6) acts as a quantum mechanical barrier that permanently prevents collapse to zero volume (R → 0). Furthermore, we calculate the photon sphere and the shadow radius for the M87* black hole, showing that our mechanical model perfectly matches the Event Horizon Telescope (EHT) observations without invoking an event horizon. Finally, we resolve the Information Paradox by proving that matter entering the Super-Star is not destroyed but mechanically fragmented and added to the mass of the star, and we provide a statistical derivation of the Bekenstein-Hawking entropy (S = A/4) from the discrete microstates of Q-balls on the star's surface, alongside falsifiable predictions for Gravitational Wave Echoes (LIGO/Virgo).