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Schwarzschild black hole singularity formation

Jorge Ovalle*

Roberto Casadio†

Alexander Kamenshchik‡

  • Research Centre for Theoretical Physics and Astrophysics, Institute of Physics, Silesian University in Opava, CZ-746 01 Opava, Czech Republic and Universidad de Tarapacá, Avenida Luis Emilio Recabarren 2477, Iquique, Chile

  • *Contact author: jorge.ovalle@physics.slu.cz
  • †Contact author: casadio@bo.infn.it
  • ‡Contact author: kamenshchik@bo.infn.it
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Phys. Rev. D 113, 064042 – Published 23 March, 2026

DOI: https://doi.org/10.1103/cbs6-d7pr

Abstract

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.

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Phys. Rev. D 113, 064042– Published 23 March, 2026
  • Received 28 October 2025
  • Accepted 6 March 2026
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