Mass (re)distribution for quantum dust cores of black holes

The collective ground state for a spherical symmetric dust ball has been investigated recently in [R. Casadio, Phys. Lett. B 843 (2023) 138055]. In this study, we refine that model by obtaining a mass distribution that accounts for the superposition of wavefunctions across different layers. The refined mass distribution shows significant deviations from the approximation without quantum superpositions. Specifically, the new nearly parabolic distribution replaces the linear mass profile of the original work, featuring an overall downward concavity, which leads to a non-vanishing tension. Notably, the regularity of the metric and causal structure are preserved in the refined analysis.