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

## TL;DR

This paper investigates the critical collapse of rotating scalar fields in 2+1 dimensions, revealing complex scaling behaviors and the lack of universal self-similar solutions, especially for non-zero angular momentum modes.

## Contribution

It provides the first detailed numerical analysis of rotating scalar field collapse in 2+1 dimensions, highlighting differences from non-rotating cases and challenging the universality of critical solutions.

## Key findings

- Ricci scaling observed across all families
- Mass scaling evidence is tentative and varies with angular momentum
- Thresholds for collapse are non-universal and depend on initial data family

## Abstract

We carry out numerical simulations of the collapse of a complex rotating scalar field of the form $\Psi(t,r,\theta)=e^{im\theta}\Phi(t,r)$, giving rise to an axisymmetric metric, in 2+1 spacetime dimensions with cosmological constant $\Lambda<0$, for $m=0,1,2$, for four 1-parameter families of initial data. We look for the familiar scaling of black hole mass and maximal Ricci curvature as a power of $|p-p_*|$, where $p$ is the amplitude of our initial data and $p_*$ some threshold. We find evidence of Ricci scaling for all families, and tentative evidence of mass scaling for most families, but the case $m>0$ is very different from the case $m=0$ we have considered before: the thresholds for mass scaling and Ricci scaling are significantly different (for the same family), scaling stops well above the scale set by $\Lambda$, and the exponents 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 the collapse threshold being controlled by a self-similar critical solution and no evidence for it being universal.