Vacuum Localized Structures: Nonsingular Black Holes and Dark-Matter Candidates

We present a vacuum-based model of nonsingular compact objects supported by a Vacuum Localized Structure (VLS): a smooth, spatially localized configuration of vacuum energy described by a Gaussian density profile. The VLS is modeled as an anisotropic vacuum stress configuration obeying the radial equation of state 𝑝𝑟=−13𝜌, with tangential stresses fixed by energy–momentum conservation. In this framework the effective gravitational source is the Tolman combination of density and pressures.Although the energy density is highest at the center, the effective gravitational source vanishes there. The dominant contribution to curvature arises from a finite-radius region where the vacuum energy density changes most rapidly. In this sense the gravitational field is generated mainly by a surrounding “vacuum shell” rather than by a central mass.Depending on the compactness, the resulting spacetimes may possess horizons or be entirely horizonless, allowing for both nonsingular black holes and ultracompact vacuum objects. Possible observational implications, including gravitational-wave echoes from horizonless configurations, are briefly discussed. Because the same type of vacuum structure can naturally extend to galactic scales, the VLS framework also provides a unified setting for compact objects and extended vacuum halos, with potential relevance for dark-matter phenomenology.