Singularities and self-similarity in gravitational collapse

TL;DR

This paper explores the role of singularities and self-similar solutions in gravitational collapse, highlighting their significance in understanding cosmic censorship violations and critical phenomena through numerical and theoretical analysis.

Contribution

It provides a unified framework linking self-similar solutions to attractors in gravitational collapse, advancing understanding of singularities and critical phenomena.

Findings

Self-similar solutions act as attractors in gravitational collapse.

Critical phenomena are related to intermediate self-similar behaviour.

Unified view of convergence and critical phenomena via renormalisation group flow.

Abstract

Einstein's field equations in general relativity admit a variety of solutions with spacetime singularities. Numerical relativity has recently revealed the properties of somewhat generic spacetime singularities. It has been found that in a variety of systems self-similar solutions can describe asymptotic or intermediate behaviour of more general solutions in an approach to singularities. The typical example is the convergence to an attractor self-similar solution in gravitational collapse. This is closely related to the cosmic censorship violation in the spherically symmetric collapse of a perfect fluid. The self-similar solution also plays an important role in critical phenomena in gravitational collapse. The critical phenomena are understood as the intermediate behaviour around a critical self-similar solution. We see that the convergence and critical phenomena are understood in a unified manner in terms of attractors of codimension zero and one, respectively, in renormalisation group flow.