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arXiv 1702.04601gr-qc
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$2+1$维旋转标量场的临界坍缩

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

Joanna Jałmużna, Carsten Gundlach

备注：
Version accepted for publication in PRD
发表信息：
Phys. Rev. D 95, 084001 (2017)
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摘要：

我们进行了数值模拟的形式$Ψ(t,r,θ)=e^{imθ}Φ(t,r)$的复杂旋转标量场的崩溃，产生一个轴对称的，在2+1时空维度与宇宙常数$Λ<0$，为$m=0,1,2$，为4个1参数的家庭的初始数据。我们寻找熟悉的黑洞质量和最大Ricci曲率的缩放作为$|p-p_*|$的幂，其中$p$是我们的初始数据的振幅和$p_*$一些阈值。我们发现了所有家族的Ricci标度的证据，以及大多数家族的质量标度的初步证据，但是$m>0$的情况与我们之前考虑过的$m=0$的情况非常不同：质量标度和Ricci标度的阈值显著不同（对于同一家族），标度在$Λ$设定的标度之上停止，指数强烈依赖于家族。因此，与$m=0$案例以及许多其他自引力系统相反，只有微弱的证据表明坍缩阈值受到自相似临界解的控制，并且没有证据表明它具有普遍性。

英文摘要：

We carry out numerical simulations of the collapse of a complex rotating scalar field of the form $Ψ(t,r,θ)=e^{imθ}Φ(t,r)$, giving rise to an axisymmetric metric, in 2+1 spacetime dimensions with cosmological constant $Λ<0$, 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 $Λ$, 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.

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