Critical phenomena of collapsing massless scalar wave packets

TL;DR

This paper develops an analytical model for the collapse of massless scalar wave packets exhibiting critical phenomena, revealing that black hole mass scales with a universal exponent in supercritical collapse.

Contribution

It introduces a self-similar analytical model for scalar wave collapse and identifies critical behavior with a specific mass scaling exponent.

Findings

Black hole mass scales as (p - p*)^γ with γ=1/2

Critical phenomena are analytically demonstrated in scalar wave collapse

Finite black hole masses are produced in supercritical collapse

Abstract

An analytical model that represents the collapse of a massless scalar wave packet with continuous self-similarity is constructed, and critical phenomena are found. In the supercritical case, the mass of black holes is finite and has the form $M \propto (p - p^{*})^{\gamma}$, with $\gamma = 1/2$.