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

TL;DR

This paper refines the quantum dust core model of black holes by deriving a mass distribution that incorporates quantum superpositions, resulting in a more accurate and physically consistent description of the black hole's internal structure.

Contribution

It introduces a new mass distribution model that accounts for quantum superpositions across layers, improving upon previous linear profiles and maintaining metric regularity.

Findings

Mass distribution becomes nearly parabolic with quantum superpositions

The refined model shows a non-vanishing tension in the core

Regularity of the metric and causal structure is preserved

Abstract

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.