Critical collapse of a spherically symmetric ultrarelativistic fluid in $2+1$ dimensions

TL;DR

This paper investigates gravitational collapse of an ultrarelativistic perfect fluid in 2+1 dimensions, revealing different critical phenomena types depending on the equation of state parameter, with detailed numerical analysis.

Contribution

It identifies and characterizes type I and type II critical phenomena in 2+1 dimensional gravitational collapse with an ultrarelativistic fluid, including the nature of the critical solutions.

Findings

Type II critical phenomena occur for .43.5.6 7 apparent horizon mass scales as a power of the distance from threshold.

Type I critical phenomena occur for .42.43 7 lifetime scales logarithmically with the distance from threshold.

The type I critical solution is static; the type II solution is non-self-similar but contracting quasi-statically.

Abstract

We carry out numerical simulations of the gravitational collapse of a perfect fluid with the ultrarelativistic equation of state $P=\kappa\rho$, in spherical symmetry in $2+1$ spacetime dimensions with $\Lambda<0$. At the threshold of prompt collapse, we find type II critical phenomena (apparent horizon mass and maximum curvature scale as powers of distance from the threshold) for $\kappa\gtrsim 0.43$, and type I critical phenomena (lifetime scales as logarithm of distance from the threshold) for $\kappa\lesssim 0.42$. The type I critical solution is static, while the type II critical solution is not self-similar (as in higher dimensions) but contracting quasi-statically.