Compressibility-Limited Threshold for Black Hole Formation in Atomic Systems

We derive a fundamental lower bound on the mass required for gravitational collapse within atomic systems. This bound is predicated solely on the inherent finite compressibility arising from interatomic spacing. In contrast to established thresholds such as the Chandrasekhar [1] or Tolman-Oppenheimer-Volkoff limits, which depend on degeneracy pressure and relativistic effects, our approach utilizes only classical considerations of gravitational confinement and physical volume. We demonstrate that while an individual atom, irrespective of its quantum state, lacks sufficient spatial structure to permit collapse, a collection of atoms introduces an effective compressible volume that scales proportionally with total mass. This analysis yields a clear, universal lower bound of approximately 6.7×10¹² kg, below which gravitational collapse into a black hole is physically precluded.