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

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 ($R^μ_ν\sim r^{-2}$) 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 ($H(t) \sim \ell_{\rm Planck}$).