On Schwarzschild black hole singularity formation

TL;DR

This paper investigates whether Schwarzschild black holes can form from smooth gravitational collapse, finding that the process involves discontinuities and singularities, implying a need for noncontinuous or quantum descriptions of black hole formation.

Contribution

It introduces a time-dependent extension of the Schwarzschild metric and demonstrates that collapse leads to discontinuities, challenging the classical view of smooth black hole formation.

Findings

Discontinuity develops at the origin during collapse.

Curvature singularities appear before the Schwarzschild point.

Spacetime smoothness breaks down, indicating noncontinuous evolution.

Abstract

We examine whether the Schwarzschild black hole can emerge as the continuous end state of gravitational collapse from a non-singular 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.