On critical behaviour in gravitational collapse

TL;DR

This paper presents a new approach to analyze critical phenomena in gravitational collapse, deriving a black hole mass formula that reveals a finite mass gap at the threshold of black hole formation.

Contribution

It introduces a method to extract black hole mass formulas from transcendental equations and provides explicit metrics describing collapse with a finite mass gap.

Findings

Black hole mass formula with a mass gap at formation threshold

Explicit asymptotically flat metrics for matter collapse

Demonstration of finite initial black hole mass

Abstract

We give an approach to studying the critical behaviour that has been observed in numerical studies of gravitational collapse. These studies suggest, among other things, that black holes initially form with infinitesimal mass. We show generally how a black hole mass formula can be extracted from a transcendental equation. Using our approach, we give an explicit one parameter set of metrics that are asymptotically flat and describe the collapse of apriori unspecified but physical matter fields. The black hole mass formula obtained from this metric exhibits a mass gap - that is, at the onset of black hole formation, the mass is finite and non-zero.