Critical Phenomena in Gravitational Collapse: The Studies So Far

TL;DR

This paper reviews the discovery and development of critical phenomena in gravitational collapse, highlighting universality, scaling laws, and analytical models, with updates on recent research and extensions to various matter fields.

Contribution

It provides a comprehensive overview of critical phenomena in gravitational collapse, including an analytical toy model and recent investigations, expanding understanding of black hole formation thresholds.

Findings

Universality and echoing in critical solutions

Power-law scaling of black hole masses

Extension of phenomena to various matter fields

Abstract

Studies of black hole formation from gravitational collapse have revealed interesting non-linear phenomena at the threshold of black hole formation. In particular, in 1993 Choptuik studied the collapse of a massless scalar field with spherical symmetry and found some behaviour, which is quite similar to the critical phenomena well-known in {\em Statistical Mechanics} and {\em Quantum Field Theory}. Universality and echoing of the critical solution and power-law scaling of the black hole masses have given rise to the name {\em Critical Phenomena in Gravitational Collapse}. Choptuik's results were soon confirmed both numerically and semi-analytically, and have extended to various other matter fields. In this paper, we shall give a brief introduction to this fascinating and relatively new area, and provides an updated publication list. An analytical "toy" model of critical collapse is presented, and some current investigations are given.