Self-Similar Solutions, Critical Behavior and Convergence to Attractor in Gravitational Collapse

TL;DR

This paper reviews self-similar solutions in gravitational collapse, emphasizing their role in critical phenomena and attractor behavior within general relativity and Newtonian gravity.

Contribution

It provides a comprehensive review of self-similar solutions and highlights their significance in understanding critical behavior and attractors in gravitational collapse.

Findings

Self-similar solutions are crucial in critical gravitational collapse.

These solutions act as attractors in the dynamics of collapse.

The review connects scale-invariance to collapse phenomena.

Abstract

General relativity as well as Newtonian gravity admits self-similar solutions due to its scale-invariance. This is a review on these self-similar solutions and their relevance to gravitational collapse. In particular, our attention is mainly paid on the crucial role of self-similar solutions in the critical behavior and attraction in gravitational collapse.