The (Unstable) Threshold of Black Hole Formation

TL;DR

This paper reviews the phenomenology of critical behavior at the threshold of black hole formation, highlighting scaling, self-similarity, and universality, and discusses the theoretical understanding of critical solutions via perturbation theory.

Contribution

It provides an overview of the diverse critical solutions in gravitational collapse and discusses their analysis through perturbation theory, connecting phenomenology with theoretical frameworks.

Findings

Identification of various critical solutions in collapse models

Connection between critical phenomena and statistical mechanics concepts

Perturbative analysis clarifies the nature of critical solutions

Abstract

In recent years it has become apparent that intriguing phenomenology exists at the threshold of black hole formation in a large class of general relativistic collapse models. This phenomenology, which includes scaling, self-similarity and universality, is largely analogous to statistical mechanical critical behaviour, a fact which was first noted empirically, and subsequently clarified by perturbative calculations which borrow on ideas and techniques from dynamical systems theory and renormalization group theory. This contribution, which closely parallels my talk at the conference, consists of an overview of the considerable ``zoo''' of critical solutions which have been discovered thus far, along with a brief discussion of how we currently understand the nature of these solutions from the point of view of perturbation theory.