Critical Phenomena in Gravitational Collapse

TL;DR

This paper reviews the discovery and understanding of critical phenomena in gravitational collapse, highlighting universality, self-similarity, and recent advances beyond spherical symmetry with implications for fundamental physics.

Contribution

It provides a comprehensive overview of critical phenomena in gravitational collapse, including recent numerical simulations and mathematical results beyond spherical symmetry.

Findings

Universality and scale invariance in black hole formation

Numerical simulations of vacuum critical collapse beyond spherical symmetry

Mathematical insights into PDE blowup and naked singularities

Abstract

As first discovered by Choptuik, the black hole threshold in the space of initial data for general relativity shows both surprising structure and surprising simplicity. Universality, power-law scaling of the black hole mass, and scale echoing have given rise to the term ``critical phenomena''. They are explained by the existence of exact solutions which are attractors within the black hole threshold, that is, attractors of codimension one in phase space, and which are typically self-similar. Critical phenomena give a natural route from smooth initial data to arbitrarily large curvatures visible from infinity, and are therefore likely to be relevant for cosmic censorship, quantum gravity, astrophysics, and our general understanding of the dynamics of general relativity. Major additions since the 2010 version of this review are numerical simulations beyond spherical symmetry, in particular of vacuum critical collapse, and new sections on mathematical results in PDE blowup (as a toy model for singularity formation) and on naked singularity formation in GR.