Critical Phenomena in Gravitational Collapse
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.
Cite
@article{arxiv.2507.07636,
title = {Critical Phenomena in Gravitational Collapse},
author = {Carsten Gundlach and David Hilditch and José M. Martín-García},
journal= {arXiv preprint arXiv:2507.07636},
year = {2025}
}
Comments
Major update to the living review available at https://doi.org/10.12942/lrr-2007-5. Feedback and suggestions very welcome, and those received by October 2025 will be considered in the version to be published. A version with new material highlighted can be rendered by downloading the source and following the instructions in the README. 51 pages, 5 figures, 1 table. arXiv admin note: text overlap with arXiv:0711.4620