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. This review gives an introduction to the phenomena, tries to summarize the essential features of what is happening, and then presents extensions and applications of this basic scenario. Critical phenomena are of interest particularly for creating surprising structure from simple equations, and for the light they throw on cosmic censorship and the generic dynamics of general relativity.
Highlights
We briefly introduce the topic of this review article in two ways: By definition, and in a historical context.1.1 Definition of the topicAn isolated system in general relativity typically ends up in one of three distinct kinds of final state
Qualitatively new phenomena were discovered, and we have reviewed this body of work by phenomena rather than by matter models
Most models in the table are restricted to spherical symmetry, and their matter content is described by a few functions of space and time
Summary
An isolated system in general relativity typically ends up in one of three distinct kinds of final state. One cannot usually tell into which basin of attraction a given data set belongs by any other method than evolving it in time to see what its final state is. The study of these invisible boundaries in phase space is the subject of the relatively new field of critical collapse. At the particular boundary between initial data that form black holes and data that disperse, scale-invariance plays an important role in the dynamics. This gives rise to a power law for the black hole mass. Critical phenomena in statistical mechanics and in gravitational collapse share scale-invariant physics and the presence of a renormalization group, but while the former involves statistical ensembles, general relativity is deterministically described by partial differential equations (PDEs)
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