论文标题
Kerr黑洞的二阶真空扰动的二阶真空扰动的数值计算
Numerical computation of second order vacuum perturbations of Kerr black holes
论文作者
论文摘要
我们的愿望是要理解围绕任意迅速旋转的Kerr黑洞的领先阶非线性引力波相互作用，我们描述了一种数值代码，旨在计算此类空间上的二阶真空扰动。我们使用的形式主义的一般讨论在（Arxiv：2008.11770）中提出；在这里，我们展示了如何通过特殊选择的坐标和四型条件来实现形式主义，并给出具有无量纲旋转参数的黑洞的示例结果$ a = 0.7 $和$ a = 0.998 $。我们首先将Teukolsky方程求解为线性扰动的Weyl标量$ψ_4^{（1）} $，然后直接重建来自$ψ_4^{（1）} $的时空度量，然后求解第二阶扰动Weyl weyl weyl salar scalar $ $ψ_4^= $ c =（2）的动态。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开发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Ringdown分析扩展到线性政权之前的分析，探索近乎远端的Kerr黑洞“湍流”的引力波“湍流”，并研究了极端质量比率的物理学。
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 $Ψ_4^{(1)}$, followed by direct reconstruction of the spacetime metric from $Ψ_4^{(1)}$, and then solve for the dynamics of the second order perturbed Weyl scalar $Ψ_4^{(2)}$. 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.
