Critical gravitational collapse with angular momentum: from critical exponents to universal scaling functions

TL;DR

This paper studies the critical behavior of gravitational collapse with angular momentum, revealing universal scaling laws and functions that describe black hole mass and angular momentum near the collapse threshold.

Contribution

It introduces a model with a spherical, self-similar critical solution with two modes, deriving universal exponents and functions for collapse with angular momentum.

Findings

Universal critical exponents for mass and angular momentum

Scaling functions analogous to ferromagnetic phase transitions

Qualitative features of high angular momentum critical collapse

Abstract

We investigate the threshold of gravitational collapse with angular momentum, under the assumption that the critical solution is spherical and self-similar and has two growing modes, namely one spherical mode and one axial dipole mode (threefold degenerate). This assumption holds for perfect fluid matter with the equation of state p=kappa rho if the constant kappa is in the range 0<kappa<1/9. There is a region in the space of initial data where the mass and angular momentum of the black hole created in the collapse are given in terms of the initial data by two universal critical exponents and two universal functions of one argument. These expressions are similar to those for the correlation length and the magnetization in a ferromagnet near its critical point, as a function of the temperature and the external magnetic field. We discuss qualitative features of the scaling functions, and hence of critical collapse with high angular momentum.