Black hole spectroscopy: Systematic errors and ringdown energy estimates
Black hole spectroscopy: Systematic errors and ringdown energy estimates
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DOI：
10.1103/physrevd.97.044048
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发表时间：
2018-02-28
影响因子：
5
通讯作者：
Khanna, Gaurav
中科院分区：
文献类型：
--
作者：
Baibhav, Vishal;Berti, Emanuele;Khanna, Gaurav
一个扭曲的黑洞松弛到它的最终状态提供了在当前和即将到来的引力波设施范围内对广义相对论的重要检验。在黑洞微扰理论中，这个阶段由指数衰减的正弦曲线（准正规模）和幂律尾的简单线性叠加组成。要以规定的精度描述波形，需要多少个拟正规模？如果只包括拟正规模而不包括尾部，我们会产生什么样的错误？在当前最先进的数值波形中还存在哪些其他系统效应？这些问题是用扭曲黑洞测试基础物理学的基础，在文献中几乎没有得到解决。我们使用数值相对论波形和黑洞微扰理论中的精确演化来提供一些答案。我们证明：（1）要使基频l = m = 2的拟正规频率和阻尼时间在1%以内或更好，至少需要包含第一泛音，最好是包含前两个或三个泛音;（ii）要确定黑洞质量和自旋的精度优于1%，就需要对任何给定的角谐模包含至少两个准正规模（l，m）。我们还改进了以前的估计和适合的振铃能量辐射在各种多极。这些结果是重要的量化理论（而不是仪器）的参数估计精度和测试的广义相对论允许振铃测量与高信噪比引力波探测器的限制。
The relaxation of a distorted black hole to its final state provides important tests of general relativity within the reach of current and upcoming gravitational wave facilities. In black hole perturbation theory, this phase consists of a simple linear superposition of exponentially damped sinusoids (the quasinormal modes) and of a power-law tail. How many quasinormal modes are necessary to describe waveforms with a prescribed precision? What error do we incur by only including quasinormal modes, and not tails? What other systematic effects are present in current state-of-the-art numerical waveforms? These issues, which are basic to testing fundamental physics with distorted black holes, have hardly been addressed in the literature. We use numerical relativity waveforms and accurate evolutions within black hole perturbation theory to provide some answers. We show that (i) a determination of the fundamental l = m = 2 quasinormal frequencies and damping times to within 1% or better requires the inclusion of at least the first overtone, and preferably of the first two or three overtones; (ii) a determination of the black hole mass and spin with precision better than 1% requires the inclusion of at least two quasinormal modes for any given angular harmonic mode (l, m). We also improve on previous estimates and fits for the ringdown energy radiated in the various multipoles. These results are important to quantify theoretical (as opposed to instrumental) limits in parameter estimation accuracy and tests of general relativity allowed by ringdown measurements with high signal-to-noise ratio gravitational wave detectors.