Numerical solution of the 2 + 1 Teukolsky equation on a hyperboloidal and horizon penetrating foliation of Kerr and application to late-time decays
Numerical solution of the 2 + 1 Teukolsky equation on a hyperboloidal and horizon penetrating foliation of Kerr and application to late-time decays
复制标题
双曲面和地平线穿透 Kerr 叶理上 2 1 Teukolsky 方程的数值解及其在晚期衰变中的应用
DOI：
10.1088/0264-9381/30/11/115013
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发表时间：
2013
影响因子：
3.5
通讯作者：
B. Bruegmann
中科院分区：
文献类型：
--
作者：
Enno Harms;S. Bernuzzi;B. Bruegmann
在这项工作中，我们给出了RáCz和Tóth最近提出的关于双曲面和透视面Kerr面层上一般自旋微扰的Teukolsky方程的公式。附加的依赖于自旋的重标度场变量可用于实现一般自旋微扰的稳定、长期和准确的时间域演化。作为应用(和严格的数值检验)，我们用2+1演化的方法研究了地平线和未来零点无限的电磁和引力扰动的后期衰变。作为初始数据，我们考虑了具有纯自旋加权球谐轮廓的(非)平稳和(非)紧支撑初始数据的四种组合。我们对轴对称微扰的后期衰变进行了广泛的研究。我们验证了解析预测的幂函数衰减率，以及幂函数指数的某种“分裂”行为。我们还给出了非轴对称微扰的结果。特别是，我们的方法允许我们研究近乎极端和极端的黑洞引力场的后期衰变行为。对于快速自转，我们观察到一个非常长的、弱衰减的准正常模相。对于极端自转，未来零点无限远处的场表现出随着时间的倒数倍衰减的振荡行为，而在地平线上，它在长时间尺度上被放大了几个数量级。这一行为可以用超辐射腔论来理解。
In this work, we present a formulation of the Teukolsky equation for generic spin perturbations on the hyperboloidal and horizon penetrating foliation of Kerr recently proposed by Rácz and Tóth. An additional, spin-dependent rescaling of the field variable can be used to achieve stable, long-term and accurate time-domain evolutions of generic spin perturbations. As an application (and a severe numerical test), we investigate the late-time decays of electromagnetic and gravitational perturbations at the horizon and future null infinity by means of 2 + 1 evolutions. As initial data we consider four combinations of (non-)stationary and (non-)compact-support initial data with a pure spin-weighted spherical harmonic profile. We present an extensive study of late-time decays of axisymmetric perturbations. We verify the power-law decay rates predicted analytically, together with a certain ‘splitting’ behaviour of the power-law exponent. We also present results for non-axisymmetric perturbations. In particular, our approach allows us to study the behaviour of the late-time decays of gravitational fields for nearly extremal and extremal black holes. For rapid rotation we observe a very prolonged, weakly damped, quasi-normal-mode phase. For extremal rotation, the field at future null infinity shows an oscillatory behaviour decaying as the inverse power of time, while at the horizon it is amplified by several orders of magnitude over long timescales. This behaviour can be understood in terms of the superradiance cavity argument.