A quantum bound on the compactness

TL;DR

This paper introduces a quantum model of gravitational collapse that constrains the size of collapsing matter, suggesting black holes are extended objects and impacting theories of quantum gravity.

Contribution

It provides a quantum framework that limits the collapse states, supporting the view that black holes are macroscopic and extended, with implications for quantum gravity and black hole models.

Findings

States with width smaller than the gravitational radius are excluded.

Black holes are shown to be macroscopic extended objects.

Implications for ultraviolet self-completion of gravity and corpuscular black hole models.

Abstract

We present a simple quantum description of the gravitational collapse of a ball of dust which excludes those states whose width is arbitrarily smaller than the gravitational radius of the matter source and supports the conclusion that black holes are macroscopic extended objects. We also comment briefly on the relevance of this result for the ultraviolet self-completion of gravity and the corpuscular picture of black holes.