Critical Behavior of Black Hole Formation in a Scalar Wave Collapse

TL;DR

This paper introduces a self-similar model for scalar wave collapse demonstrating black hole formation only in strong-field conditions and compares the critical behavior with numerical simulations.

Contribution

It provides a new self-similar analytical model for scalar field collapse and links it to numerical findings by Choptuik.

Findings

Black hole formation occurs only for p > 1

Critical behavior matches numerical results as p approaches 1

Model elucidates conditions for black hole formation in scalar collapse

Abstract

We present a self-similar model of spherically symmetric collapse of a massless scalar field with a parameter $p$. The black hole formation is explicitly shown to occur only in the strong-field implosion of $p >1$. The field evolution in the critical limit $ p \rightarrow 1 $ is compared with numerical results found by Choptuik.