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 $h=2M$, demonstrating how trapped surfaces form dynamically in finite time, and (ii) a {naked-}singularity resolution, where an integrable Ricci curvature singularity ($R_{\nu }^{\mu }\sim r^{-2}$) 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 ($H(t)\sim {\ell }_{\mathrm{Planck}}$).

10 pages, 4 figures, Published version

References in corpus (28)

• First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole
• First Sagittarius A* Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole in the Center of the Milky Way
• Naked Singularities in Spherically Symmetric Inhomogeneous Tolman-Bondi Dust Cloud Collapse
• Recent developments in gravitational collapse and spacetime singularities
• Why do naked singularities form in gravitational collapse?
• Black hole collapse and bounce in effective loop quantum gravity
• Quantum gravity of dust collapse: shock waves from black holes
• Singularity avoidance for collapsing quantum dust in the Lemaitre-Tolman-Bondi model
• Quantum gravitational collapse: non-singularity and non-locality
• Space-Times with Integrable Singularity
• Black hole singularity resolution via the modified Raychaudhuri equation in loop quantum gravity
• Schrodinger formalism, black hole horizons and singularity behavior
• Generalized Lemaitre-Tolman-Bondi Solutions with Pressure
• Strong curvature naked singularities in spherically symmetric perfect fluid collapse
• Quantum Oppenheimer-Snyder model
• Gravitational collapse of barotropic spherical fluids
• Conserved charges in general relativity
• Black hole formation in perfect fluid collapse
• Schwarzschild black hole revisited: Before the complete collapse
• Black holes without Cauchy horizons and integrable singularities
• Gravitational collapse in effective loop quantum gravity: beyond marginally bound configurations
• Criteria for energy conditions
• Configurational entropy of black hole quantum cores
• Trapped surfaces in Oppenheimer-Snyder black holes
• Conserved non-Noether charge in general relativity: Physical definition vs. Noether's 2nd theorem
• Cosmology from Schwarzschild black hole revisited
• Physical and Theoretical Challenges to Integrable Singularities
• On Schwarzschild black hole singularity formation