A quantum bound on the compactness

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.
Comment: 8 pages, LaTeX, one figure, references and comments added