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

until reaching its final size

$$h=2\mathcal{M}$$ h = 2 M

, demonstrating how trapped surfaces form dynamically in finite time, and (ii) a naked-singularity resolution, where an integrable Ricci curvature singularity (

$$R^\mu {}_\nu \sim r^{-2}$$ R μ ν ∼ r - 2

) develops at

$$r=0$$ 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 (

$$H(t) \sim \ell _\textrm{Planck}$$ H ( t ) ∼ ℓ Planck

).