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We carry out numerical simulations of the collapse of a complex rotatingscalar field of the form $\Psi(t,r,\theta)=e^{im\theta}\Phi(t,r)$, giving riseto an axisymmetric metric, in 2+1 spacetime dimensions with cosmologicalconstant $\Lambda<0$, for $m=0,1,2$, for four 1-parameter families of initialdata. We look for the familiar scaling of black hole mass and maximal Riccicurvature as a power of $|p-p_*|$, where $p$ is the amplitude of our initialdata and $p_*$ some threshold. We find evidence of Ricci scaling for allfamilies, and tentative evidence of mass scaling for most families, but thecase $m>0$ is very different from the case $m=0$ we have considered before: thethresholds for mass scaling and Ricci scaling are significantly different (forthe same family), scaling stops well above the scale set by $\Lambda$, and theexponents depend strongly on the family. Hence, in contrast to the $m=0$ case,and to many other self-gravitating systems, there is only weak evidence for thecollapse threshold being controlled by a self-similar critical solution and noevidence for it being universal.

Critical collapse of a rotating scalar field in $2+1$ dimensions