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arXiv · 2607.08088

An analytic model for a total process of gravitational collapse: From star to Schwarzschild black hole

Sinya Aoki·Jorge Ovalle
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Abstract

We present an exact analytical model describing a complete gravitational collapse of matter from horizonless initial conditions to black hole formation, tracing the full evolution of the horizon $H(t)$ from its formation at microscopic scales to macroscopic stabilization. The solution reveals two main stages: (i) a dynamical horizon growth, where an apparent horizon $H(t)$ emerges at a critical time $t_b$ until reaching its final size $h=2 M$, demonstrating how trapped surfaces form dynamically in finite time, and (ii) a {naked-}singularity resolution, where an integrable Ricci curvature singularity ($R^\mu{}_\nu \sim r^{-2}$) develops at $r=0$, but remains causally hidden by the horizon growth, preserving weak cosmic censorship without exotic matter. The model could offer a framework to study the quantum-to-classical transition ($H(t) \sim \ell_{\rm Planck}$).

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Sinya Aoki, Jorge Ovalle. 2026-07-09. An analytic model for a total process of gravitational collapse: From star to Schwarzschild black hole. https://doi.org/10.1140/epjc%2Fs10052-026-16050-y

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