Critical gravitational collapse with angular momentum II: soft equations of state

TL;DR

This paper investigates critical phenomena in rotating ultrarelativistic perfect fluid collapse with various equations of state, revealing how additional unstable modes influence black hole formation and properties near the threshold.

Contribution

It extends previous studies to a broader range of equations of state, analyzing the effects of angular momentum and unstable modes on critical collapse and black hole characteristics.

Findings

Critical solution has one unstable mode for certain 7 values.

An additional unstable axial mode appears for 7<1/9.

Systematic effects observed in black-hole angular momentum.

Abstract

We study critical phenomena in the collapse of rotating ultrarelativistic perfect fluids, in which the pressure $P$ is related to the total energy density $\rho$ by $P=\kappa\rho$, with $\kappa$ a constant. We generalize earlier results for radiation fluids with $\kappa=1/3$ to other values of $\kappa$, focussing on $\kappa < 1/9$. For $1/9<\kappa \lesssim 0.49$, the critical solution has only one unstable, growing mode, which is spherically symmetric. For supercritical data it controls the black hole mass, while for subcritical data it controls the maximum density. For $\kappa<1/9$, an additional axial $l=1$ mode becomes unstable. This controls either the black hole angular momentum, or the maximum angular velocity. In theory, the additional unstable $l=1$ mode changes the nature of the black hole threshold completely: at sufficiently large initial rotation rates $\Omega$ and sufficient fine-tuning of the initial data to the black hole threshold we expect to observe nontrivial universal scaling functions (familiar from critical phase transitions in thermodynamics) governing the black hole mass and angular momentum, and, with further fine-tuning, eventually a finite black hole mass almost everywhere on the threshold. In practice, however, the second unstable mode grows so slowly that we do not observe this breakdown of scaling at the level of fine-tuning we can achieve, nor systematic deviations from the leading-order power-law scalings of the black hole mass. We do see systematic effects in the black-hole angular momentum, but it is not clear yet if these are due to the predicted non-trivial scaling functions, or to nonlinear effects at sufficiently large initial angular momentum (which we do not account for in our theoretical model).