How a Matter-to-Vacuum Phase Transition Can Prevent Black-Hole Singularities

The appearance of spacetime singularities during gravitational collapse remains one of the most important unresolved problems of General Relativity. In the standard picture, continued compression of matter inside a black hole leads to divergent densities, divergent spacetime curvature, and the breakdown of the classical gravitational description. In this work, we investigate an alternative phenomenological scenario in which gravitational collapse triggers a density-induced matter-to-vacuum phase transition once a critical density is reached. We assume that above this threshold ordinary matter is rapidly converted into a Vacuum Localized Structure (VLS) phase, representing a localized vacuum state that carries the mass-energy of the original collapsing matter. The detailed microscopic mechanism responsible for the transition is not specified. Instead, the transition is treated as an effective process that replaces the collapsing matter by a compact vacuum structure while conserving the total mass-energy of the system. The post-transition object is modeled as a static, spherically symmetric equilibrium configuration governed by the Einstein field equations and the Tolman-Oppenheimer-Volkoff equation. A Gaussian density distribution is adopted for the VLS phase, leading to finite central density, finite pressure, and a regular mass profile throughout the interior. The characteristic size of the VLS core follows directly from mass conservation and is uniquely determined by the total mass and the critical transition density. The resulting solutions replace the classical black-hole singularity by a finite-curvature core. The mass function approaches zero smoothly at the center, preventing the divergent gravitational compression associated with conventional collapse solutions. Consequently, all curvature invariants remain finite and the spacetime remains regular throughout the interior region. In this sense, the phase transition acts as a gravitational regulator, replacing continued compression by a stable vacuum-supported equilibrium configuration. Within this framework, singularity avoidance emerges without modification of the Einstein field equations and without the introduction of an explicit de Sitter vacuum core.