1.2 Historical introduction1 Introduction1 Introduction

1.1 Definition of the topic

An isolated system in general relativity typically ends up in one of three distinct kinds of final state. It either collapses to a black hole, forms a stable star, or explodes and disperses, leaving empty flat spacetime behind. The phase space of isolated gravitating systems is therefore divided into basins of attraction. 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.

Ideas from dynamical systems theories provide a qualitative understanding of the time evolution of initial data near any of these boundaries. 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. Scale-invariance, universality and power-law behavior suggest the name ``critical phenomena in gravitational collapse''.

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).

1.2 Historical introduction1 Introduction1 Introduction

image Critical Phenomena in Gravitational Collapse
Carsten Gundlach
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