Superradiant instabilities of rotating black holes in the time domain
Superradiant instabilities of rotating black holes in the time domain
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DOI：
10.1103/physrevd.87.124026
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发表时间：
2012-12
影响因子：
5
通讯作者：
S. Dolan
中科院分区：
文献类型：
--
作者：
S. Dolan
旋转黑洞时空上的玻色子场会受到超辐射的放大，这会在两种情况下引起指数增长的不稳定性（“黑洞炸弹”）：如果黑洞被镜子包围，或者如果玻色子场具有静止质量。在这里，我们提出了克尔时空标量场的时域研究，探测高达 t≲5×106M 的超长时间尺度，以揭示不稳定性的增长。我们描述了一种高效的场演化方法，该方法基于将谱分解为一组耦合的 1+1D 方程，以及受“完美匹配层”范式启发的吸收边界条件。首先，我们检查镜子的情况，以研究不稳定性时间尺度和模式结构如何取决于镜子半径。接下来，我们检查大范围的场，其丰富的频谱（通过傅里叶分析揭示）会产生“跳动”效应，从而掩盖了不稳定性。我们表明，通过跟踪外部时空场的应力能量，可以清楚地揭示不稳定性。我们通过应用频率滤波器来隔离各个模态对时域信号的贡献，计算一系列质量耦合的增长率。我们的结果与之前的频域研究一致，该研究将克尔时空中的大标量场的最大增长率设定为τ-1≈1.72×10-7(GM/c3)-1。
Bosonic fields on rotating black hole spacetimes are subject to amplification by superradiance, which induces exponentially-growing instabilities (the “black hole bomb”) in two scenarios: if the black hole is enclosed by a mirror, or if the bosonic field has rest mass. Here we present a time-domain study of the scalar field on Kerr spacetime which probes ultra-long timescales up to t≲5×106M, to reveal the growth of the instability. We describe a highly-efficient method for evolving the field, based on a spectral decomposition into a coupled set of 1+1D equations, and an absorbing boundary condition inspired by the “perfectly-matched layers” paradigm. First, we examine the mirror case to study how the instability timescale and mode structure depend on mirror radius. Next, we examine the massive-field, whose rich spectrum (revealed through Fourier analysis) generates “beating” effects which disguise the instability. We show that the instability is clearly revealed by tracking the stress-energy of the field in the exterior spacetime. We calculate the growth rate for a range of mass couplings, by applying a frequency-filter to isolate individual modal contributions to the time-domain signal. Our results are in accord with previous frequency-domain studies which put the maximum growth rate at τ-1≈1.72×10-7(GM/c3)-1 for the massive scalar field on Kerr spacetime.