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

We carry out numerical simulations of the gravitational collapse of a perfect fluid with the ultrarelativistic equation of state P = kappa p, 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 greater than or similar to 0.43, and type I critical phenomena (lifetime scales as logarithm of distance from the threshold) for kappa less than or similar to 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 quasistatically.