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

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 $|p-p_{\ast }|$, where $p$ is the amplitude of our initial data and $p_{\ast }$ 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.

Version accepted for publication in PRD

References in corpus (1)

• Scalar field critical collapse in 2+1 dimensions

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