This study presents the mathematical derivation of Vacuum Localized Strctures (VLS), gravitationally stable spacetime structures, as an alternative to dark matter. Assuming galaxies are embedded in galactic-sized VLS, the observed flat galaxy rotation curves can be explained without requiring the standard dark matter halo. This concept has been applied to the case of the Milky Way and profiles of density, pressure and rotation velocity have been derived, demonstrating a close correspondence with the observations. The VLS Gaussian density profile naturally explains the flat central density cores observed in dwarf galaxies, providing a compelling solution to the core-cusp problem. Furthermore, the early formation of VLS shortly after the Big Bang offers a framework for understanding the rapid emergence of massive galaxies, addressing the challenges posed by recent James Webb Space Telescope observations. These findings suggest that VLS could serve as both the gravitational scaffolding for galaxy formation and a replacement for cold dark matter, unifying multiple cosmological phenomena under a single theoretical framework.
R. Van Nieuwenhove (Mon,) studied this question.