Critical Collapse of Einstein Cluster

TL;DR

This paper investigates the critical behavior in the gravitational collapse of Einstein Clusters, revealing a phase transition between black hole formation and dispersal, with a specific mass scaling law near the threshold.

Contribution

It analytically and numerically demonstrates the existence of critical phenomena and mass scaling in Einstein Cluster collapse, identifying the critical exponent as 3/2.

Findings

Critical phenomena observed in Einstein Cluster collapse.

Mass of black holes follows a 3/2 power-law scaling near criticality.

Existence of parameter ranges avoiding shell-crossing issues.

Abstract

We observe critical phenomena in spherically symmetric gravitational collapse of Einstein Cluster. We show analytically that the collapse evolution ends either in formation of a black hole or in dispersal depending on the values of initial parameters which characterize initial density and angular momentum of the collapsing cloud. Near the threshold of black hole formation, we obtain scaling relation for the mass of the black hole and find the critical exponent value to be 3/2. We numerically confirm that there exist wide ranges of initial parameter values around the critical configuration for which the model remains shell-crossing free.