Numerical computation of second-order vacuum perturbations of Kerr black holes
Numerical computation of second-order vacuum perturbations of Kerr black holes
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DOI：
10.1103/physrevd.103.104018
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发表时间：
2020-10
影响因子：
5
通讯作者：
Justin L. Ripley;N. Loutrel;Elena Giorgi;F. Pretorius
中科院分区：
文献类型：
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作者：
Justin L. Ripley;N. Loutrel;Elena Giorgi;F. Pretorius
为了理解任意快速旋转的克尔黑洞周围的阶非线性引力波相互作用，我们描述了一个旨在计算这种时空上的二阶真空摄动的数值代码。关于我们使用的形式主义的一般性讨论在（arXiv:2008.11770）中提出；在这里，我们展示了如何用特定的坐标选择和四分体条件在数值上实现这种形式，并给出了无量纲自旋参数$a=0.7$和$a=0.998$的黑洞的示例结果。首先求解线性摄动Weyl标量$\Psi_4^{(1)}$的Teukolsky方程，然后直接从$\Psi_4^{(1)}$重建时空度规，然后求解二阶摄动Weyl标量$\Psi_4^{(2)}$的动力学。该代码是迈向更通用的二阶代码的第一步，我们概述了如何进一步发展我们的基本方法来解决当前感兴趣的问题，包括将黑洞合并中的环溃分析扩展到线性制度之前，探索近极值克尔黑洞周围的引力波“湍流”，以及研究极端质量比启发的物理学。
Motivated by the desire to understand the leading order nonlinear gravitational wave interactions around arbitrarily rapidly rotating Kerr black holes, we describe a numerical code designed to compute second order vacuum perturbations on such spacetimes. A general discussion of the formalism we use is presented in (arXiv:2008.11770); here we show how we numerically implement that formalism with a particular choice of coordinates and tetrad conditions, and give example results for black holes with dimensionless spin parameters $a=0.7$ and $a=0.998$. We first solve the Teukolsky equation for the linearly perturbed Weyl scalar $\Psi_4^{(1)}$, followed by direct reconstruction of the spacetime metric from $\Psi_4^{(1)}$, and then solve for the dynamics of the second order perturbed Weyl scalar $\Psi_4^{(2)}$. This code is a first step toward a more general purpose second order code, and we outline how our basic approach could be further developed to address current questions of interest, including extending the analysis of ringdown in black hole mergers to before the linear regime, exploring gravitational wave "turbulence" around near-extremal Kerr black holes, and studying the physics of extreme mass ratio inspiral.