Critical collapse of an axisymmetric ultrarelativistic fluid in $2+1$ dimensions

TL;DR

This paper investigates the gravitational collapse of rotating ultrarelativistic fluids in 2+1 dimensions, revealing different critical phenomena types depending on the equation of state parameter and angular momentum.

Contribution

It provides the first numerical analysis of critical collapse phenomena for rotating ultrarelativistic fluids in 2+1 dimensions, identifying conditions for type I and type II behaviors.

Findings

Type I critical phenomena occur for .42 .42 in .43, with stationary and quasistationary solutions.

The spin-to-mass ratio of the critical solution increases during contraction.

Extremal black holes are avoided as contraction ends smoothly near extremality.

Abstract

We carry out numerical simulations of the gravitational collapse of a rotating perfect fluid with the ultrarelativistic equation of state $P=\kappa\rho$, in axisymmetry in $2+1$ spacetime dimensions with $\Lambda<0$. We show that for $\kappa \lesssim 0.42$, the critical phenomena are type I and the critical solution is stationary. The picture for $\kappa \gtrsim 0.43$ is more delicate: for small angular momenta, we find type II phenomena and the critical solution is quasistationary, contracting adiabatically. The spin-to-mass ratio of the critical solution increases as it contracts, and hence so does that of the black hole created at the end as we fine-tune to the black-hole threshold. Forming extremal black holes is avoided because the contraction of the critical solution smoothly ends as extremality is approached.