Minimum black hole mass from colliding Gaussian packets

TL;DR

This paper investigates the minimum mass required for black hole formation from colliding Gaussian packets, using a simplified horizon formation criterion to relate the packets' width to black hole mass, with implications for classical, quantum, and extra-dimensional physics.

Contribution

It introduces a simple approximation to determine the minimum black hole mass based on packet width, without detailed dynamical evolution, applicable to various physical contexts.

Findings

Minimum black hole mass depends on the width of Gaussian packets.

A horizon forms when the mass exceeds half the areal radius in the model.

Implications discussed for classical, quantum, and extra-dimensional theories.

Abstract

We study the formation of a black hole in the collision of two Gaussian packets. Rather than following their dynamical evolution in details, we assume a horizon forms when the mass function for the two packets becomes larger than half the flat areal radius, as it would occur in a spherically symmetric geometry. This simple approximation allows us to determine the existence of a minimum black hole mass solely related to the width of the packets. We then comment on the possible physical implications, both in classical and quantum physics, and models with extra spatial dimensions.