# Critical Phenomena in Gravitational Collapse

and

**José M. Martín-García
**
Institut d’Astrophysique de Paris CNRS & Université Pierre et Marie Curie,

98 bis boulevard Arago, 75014 Paris, France

Laboratoire Univers et Théories CNRS & Université Paris Diderot,

5 place Jules Janssen, 92190 Meudon, France

http://metric.iem.csic.es/Martin-Garcia/
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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.