Late time dynamics of rapidly rotating black holes
Late time dynamics of rapidly rotating black holes
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DOI：
10.1103/physrevd.64.104021
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发表时间：
2001-03
影响因子：
5
通讯作者：
K. Glampedakis;N. Andersson
中科院分区：
文献类型：
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作者：
K. Glampedakis;N. Andersson
我们研究了一个动态摄动的快速旋转黑洞的晚时行为。考虑到一个极端的克尔黑洞，我们表明，大量几乎无阻尼的准正态模式（存在于方位角特征值m的非零值）以这样一种方式组合，即场（如在无穷远处观察到的）以在晚时间衰减为1/t的振幅振荡。这与非旋转黑洞研究中常见的标准晚时间幂律衰减形成鲜明对比。然而，这种长寿命的振荡“尾巴”不会出现在非极端（可能与天体物理学更相关）黑洞中，因为我们发现许多准正态模式（单独激发到非常小的振幅）结合在一起产生指数衰减场。在非常晚的时候，这种缓慢衰减的准不规则模式信号让位于标准幂律尾部（对应于依赖于初始数据的多极混合）。这些结果可能对探测来自快速旋转黑洞的引力波信号有意义，因为所需的理论模板需要从许多模式的线性组合中构建。我们的主要结果是解析得到的，但是我们用Teukolsky方程的数值时间演化来支持我们的结论。这些时间演化提供了一个有趣的见解，即准正态模式可以被视为困在视界外时空区域的波。他们还提出，对于我们观察到的极端黑洞的行为，一个合理的机制是，黑洞外存在一个“超辐射共振腔”。
We study the late-time behavior of a dynamically perturbed rapidly rotating black hole. Considering an extreme Kerr black hole, we show that the large number of virtually undamped quasinormal modes (that exist for nonzero values of the azimuthal eigenvalue m) combine in such a way that the field (as observed at infinity) oscillates with an amplitude that decays as 1/t at late times. This is in clear contrast to the standard late time power-law falloff familiar from studies of nonrotating black holes. This long-lived oscillating “tail” will, however, not be present for nonextreme (presumably more astrophysically relevant) black holes, for which we find that many quasinormal modes (individually excited to a very small amplitude) combine to give rise to an exponentially decaying field. At very late times this slowly damped quasinormal-mode signal gives way to the standard power-law tail (corresponding to a mixture of multipoles depending on the initial data). These results could have implications for the detection of gravitational-wave signals from rapidly spinning black holes, since the required theoretical templates need to be constructed from linear combinations of many modes. Our main results are obtained analytically, but we support the conclusions with numerical time evolutions of the Teukolsky equation. These time evolutions provide an interesting insight into the notion that the quasinormal modes can be viewed as waves trapped in the spacetime region outside the horizon. They also suggest that a plausible mechanism for the behavior we observe for extreme black holes is the presence of a “superradiance resonance cavity” immediately outside the black hole.