Numerical study of the quasinormal mode excitation of Kerr black holes
Numerical study of the quasinormal mode excitation of Kerr black holes
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DOI：
10.1103/physrevd.74.084028
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发表时间：
2006-08
影响因子：
5
通讯作者：
Ernst Nils Dorband;E. Berti;P. Diener;E. Schnetter;M. Tiglio
中科院分区：
文献类型：
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作者：
Ernst Nils Dorband;E. Berti;P. Diener;E. Schnetter;M. Tiglio
我们提出了克尔黑洞标量扰动的三维演化的数值结果。我们的模拟利用高阶精确多块代码，自然地允许适应网格和平滑的内部（切除）和外部边界。我们专注于准正规振铃相位，提出了一种提取准正规模式频率和幅度的系统方法，并将我们的结果与微扰理论进行比较。检测振铃波形中的单一模式可以测量黑洞的质量和自旋；多模式检测将允许测试源的克尔性质。由于多模式检测的可能性取决于相对模式幅度，因此我们详细研究了这个主题。每种模式的幅度以指数方式取决于拟正态状态的开始时间，这没有明确定义。我们表明，可以通过考虑适当选择的相对模式振幅来规避这种时移问题。从我们的模拟中，我们提取了同向旋转和反向旋转模式的准正常频率以及相对和绝对振幅（包括同向旋转情况下的泛音）。我们研究这些振幅对初始扰动形状的依赖性、模式的角度依赖性以及黑洞自旋，并与所谓的渐近近似中的扰动理论的结果进行比较。我们还将数值模拟的准正态频率与微扰理论的预测进行了比较，发现两者非常吻合。对于快速旋转的黑洞（自旋 j=0.98），我们不仅可以提取基模的准正常频率，还可以提取前两个泛音的准正常频率。最后，我们研究在什么条件下给定模式对之间的相对振幅获得最大激发，并对旋转模式-模式耦合进行定量分析。我们分析的主要结论和技术非常普遍，因此，应该对天体物理引力波源产生的振铃引力波的研究感兴趣。 « less
We present numerical results from three-dimensional evolutions of scalar perturbations of Kerr black holes. Our simulations make use of a high-order accurate multiblock code which naturally allows for adapted grids and smooth inner (excision) and outer boundaries. We focus on the quasinormal ringing phase, presenting a systematic method for extraction of the quasinormal mode frequencies and amplitudes and comparing our results against perturbation theory. The detection of a single mode in a ringdown waveform allows for a measurement of the mass and spin of a black hole; a multimode detection would allow a test of the Kerr nature of the source. Since the possibility of a multimode detection depends on the relative mode amplitude, we study this topic in some detail. The amplitude of each mode depends exponentially on the starting time of the quasinormal regime, which is not defined unambiguously. We show that this time-shift problem can be circumvented by looking at appropriately chosen relative mode amplitudes. From our simulations we extract the quasinormal frequencies and the relative and absolute amplitudes of corotating and counterrotating modes (including overtones in the corotating case). We study the dependence of these amplitudes on the shape of the initial perturbation, the angular dependencemore » of the mode, and the black hole spin, comparing against results from perturbation theory in the so-called asymptotic approximation. We also compare the quasinormal frequencies from our numerical simulations with predictions from perturbation theory, finding excellent agreement. For rapidly rotating black holes (of spin j=0.98) we can extract the quasinormal frequencies of not only the fundamental mode, but also of the first two overtones. Finally we study under what conditions the relative amplitude between given pairs of modes gets maximally excited and present a quantitative analysis of rotational mode-mode coupling. The main conclusions and techniques of our analysis are quite general and, as such, should be of interest in the study of ringdown gravitational waves produced by astrophysical gravitational wave sources.« less