The Critical Mass-Limit in Black Hole Evolution: A Prediction of Unified Fractal Quantum Field

Abstract

The prevailing view of black holes in classical general relativity permits unbounded growth, culminating in a singular, physics-breaking endpoint. While quantum gravity approaches aim to resolve the singularity, the question of a fundamental upper mass limit remains open. This paper presents a novel theoretical framework based on a Unified Fractal Quantum Field Theory (UFQFT) that predicts a natural saturation point for black hole mass. By reinterpreting the black hole interior not as a singularity but as a fractal core where the wavefunctions of constituent quarks and particles merge into a single, cohesive structure, we derive an effective repulsive Ψ-charge. We demonstrate that the gravitational pressure () and this repulsive pressure (​) achieve equilibrium at a critical charge-to-mass ratio =≈8.62×10⁻¹¹C/kg. This balance implies a critical mass (​) for any black hole, beyond which growth is halted by a prospective bounce or mass-shedding phase transition. We parameterize the mass dependence of the effective repulsion, α(M), and show how  can be tuned to align with astrophysical observations, from stellar-mass to supermassive black holes. Our model not only offers a mechanism to evade the singularity but also provides testable predictions for the black hole mass spectrum and the extreme activity of quasars, potentially explaining why black holes cannot grow indefinitely.