Analytical solutions for black-hole critical behaviour

TL;DR

This paper derives an exact self-similar solution describing the critical collapse behavior of a spherical Einstein cluster, revealing the formation of a naked singularity and the transition to a static configuration.

Contribution

It provides the first analytical self-similar solution at the black-hole critical threshold for a dynamical Einstein cluster.

Findings

Identifies a unique self-similar solution at the collapse threshold.

Shows the solution involves a naked singularity formation.

Demonstrates the solution approaches a static cluster asymptotically.

Abstract

Dynamical Einstein cluster is a spherical self-gravitating system of counterrotating particles, which may expand, oscillate and collapse. This system exhibits critical behaviour in its collapse at the threshold of black hole formation. It appears when the specific angular momentum of particles is tuned finely to the critical value. We find the unique exact self-similar solution at the threshold. This solution begins with a regular surface, involves timelike naked singularity formation and asymptotically approaches a static self-similar cluster.