Non-Universality of Critical Behaviour in Spherically Symmetric Gravitational Collapse

TL;DR

This paper investigates the non-universal critical behavior in spherically symmetric gravitational collapse of a perfect fluid, showing that the critical index varies significantly with the equation of state parameter.

Contribution

It provides a simple expression for the critical index and demonstrates its dependence on the equation of state parameter, challenging the universality of critical phenomena in gravitational collapse.

Findings

Critical index $gamma varies with parameter $k$

Critical behavior is non-universal across different equations of state

Provides a simple formula for the critical index

Abstract

The aim of the present letter is to explain the `critical behaviour' observed in numerical studies of spherically symmetric gravitational collaps of a perfect fluid. A simple expression results for the critical index $\gamma$ of the black hole mass considered as an order parameter. $\gamma$ turns out to vary strongly with the parameter $k$ of the assumed equation of state $p=k\rho$.