Horizon Quantum Mechanics of collapsing shells

TL;DR

This paper investigates the quantum probability of horizon formation during shell collisions, revealing interference effects and aligning with classical conjectures, thereby advancing the quantum understanding of black hole formation.

Contribution

It introduces a quantum horizon wave-function approach to analyze shell collisions, highlighting interference effects and extending previous models of black hole formation.

Findings

Probability of horizon formation modulates with shell momenta and collision radius.

Quantum interference manifests in the horizon formation probability.

Results qualitatively agree with the hoop conjecture and quantum uncertainty principles.

Abstract

We study the probability that a horizon appears when concentric shells of matter collide, by computing the horizon wave-function of the system. We mostly consider the collision of two ultra-relativistic shells, both shrinking and expanding, at the moment their radii are equal, and find a probability that the system is a black hole which is in qualitative agreement with what one would expect according to the hoop conjecture and the uncertainty principle of quantum physics, and parallels the results obtained for simpler sources. One new feature however emerges, in that this probability shows a modulation with the momenta of the shells and the radius at which the shells collide, as a manifestation of quantum mechanical interference. Finally, we also consider the case of one light shell collapsing into a larger central mass.