Schwarzschild black hole singularity formation

We examine whether the Schwarzschild black hole can emerge as the continuous end state of gravitational collapse from a nonsingular configuration. Employing a time-dependent extension of the regular Schwarzschild metric, we track the evolution of the geometry during collapse and find that the process cannot remain continuous. The metric function develops a discontinuity at the origin, marking a breakdown of spacetime smoothness, an effect identified as “Minkowski breaking.” Before the Schwarzschild point source can form at r =0, curvature singularities appear, and the Cauchy horizon disappears. These results strongly suggest that spacetime may not evolve smoothly toward the Schwarzschild geometry. Instead, the formation of a Schwarzschild black hole appears to entail a discrete change in the structure of spacetime, pointing to the need for a noncontinuous, possibly quantized, framework to describe the emergence or regularization of gravitational singularities.