Critical collapse of ultrarelativistic fluids: Damping or growth of aspherical deformations
Critical collapse of ultrarelativistic fluids: Damping or growth of aspherical deformations
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DOI：
10.1103/physrevd.98.024053
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发表时间：
2018-05
影响因子：
5
通讯作者：
Juliana Celestino;T. Baumgarte
中科院分区：
文献类型：
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作者：
Juliana Celestino;T. Baumgarte
我们进行了完全非线性数值模拟，以研究超相对论流体引力坍缩中临界自相似解的非球面变形。采用微扰计算，冈拉克预测这些微扰的行为类似于阻尼振荡或增长振荡，频率和阻尼（或增长）率取决于状态方程。我们考虑了一些不同的状态方程和程度的非球面性，并找到非常好的协议与Gundlach的研究结果为极性$\ensuremath {\ell}= 2 $模式。对于足够软的状态方程，模式阻尼，这意味着，在完美的微调的限制，球对称的临界解被恢复。我们发现，非球面的程度上的频率和阻尼参数或在幂律标度的临界指数最多有一个小的影响。我们的研究结果也证实了，第一次，冈拉克的预测，$\ensuremath {\ell}= 2 $模式变得不稳定的足够刚性的状态方程。在这种情况下，球对称自相似解不再能通过微调到黑洞阈值来恢复，人们也不再期望幂律标度能保持任意小的尺度。
We perform fully nonlinear numerical simulations to study aspherical deformations of the critical self-similar solution in the gravitational collapse of ultrarelativistic fluids. Adopting a perturbative calculation, Gundlach predicted that these perturbations behave like damped or growing oscillations, with the frequency and damping (or growth) rates depending on the equation of state. We consider a number of different equations of state and degrees of asphericity and find very good agreement with the findings of Gundlach for polar $\ensuremath{\ell}=2$ modes. For sufficiently soft equations of state, the modes are damped, meaning that, in the limit of perfect fine-tuning, the spherically symmetric critical solution is recovered. We find that the degree of asphericity has at most a small effect on the frequency and damping parameter or on the critical exponents in the power-law scalings. Our findings also confirm, for the first time, Gundlach's prediction that the $\ensuremath{\ell}=2$ modes become unstable for sufficiently stiff equations of state. In this regime, the spherically symmetric self-similar solution can no longer be recovered by fine-tuning to the black-hole threshold, and one can no longer expect power-law scaling to hold to arbitrarily small scales.