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arXiv 2406.11986gr-qcastro-ph.COastro-ph.HEastro-ph.IM
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通过 METRICS 研究修正引力中任意次极端自旋黑洞的准正模频率与引力微扰：scalar-Gauss-Bonnet 引力情形

Quasi-normal mode frequencies and gravitational perturbations of black holes with any subextremal spin in modified gravity through METRICS: the scalar-Gauss-Bonnet gravity case

Adrian Ka-Wai Chung, Nicolas Yunes

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Matched the published version; abstract trimmed, please refer to the PDF for the full abstract; 24 pages, 8 figures, 6 tables
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AI总结：

本文扩展 METRICS 谱方法，在不解耦线性化场方程的情况下计算 scalar-Gauss-Bonnet 引力中快速旋转黑洞的引力准正模频率及度规微扰修正。

摘要：

双黑洞并合铃宕阶段发出的引力波是研究强引力的独特探针。然而，理解偏离广义相对论的效应如何影响黑洞铃宕阶段极具挑战性，因为这需要求解高度耦合、有时甚至是高阶的偏微分方程。本文扩展了一种新方法，即 Metric pErTuRbations wIth speCtral methodS（METRICS，基于谱方法的度规微扰），用于研究修正引力中鸣响黑洞的度规微扰和准正模频率。我们首先推导了广义相对论之外旋转黑洞在事件视界和空间无穷远处度规微扰的渐近行为。随后，我们扩展了 METRICS 的特征值微扰理论方法，使其能够计算准正模频率和度规微扰的领先阶修正引力修正。我们将 METRICS 应用于 scalar-Gauss-Bonnet 引力中的旋转黑洞。在不对该理论中的线性化场方程进行解耦或简化的情况下，我们计算了 a≤0.85 黑洞的 nlm=022、021 和 033 模的轴向与极向微扰准正频率的领先阶修正。对于所有研究的模，METRICS 所得频率的数值精度在 a≤0.6 时为≤10^-5，在 0.6<a≤0.7 时为≲10^-4，在 0.7<a≤0.85 时为≲10^-2。我们将频率拟合为自旋的多项式，其系数（至自旋二阶）与以往慢旋转近似所得结果一致。这些结果首次准确计算了 scalar-Gauss-Bonnet 引力中快速旋转黑洞（a∼0.85）的引力准正模频率。

英文摘要：

The gravitational waves emitted in the ringdown phase of binary black-hole coalescence are a unique probe of strong gravity. Understanding how deviations from general relativity affect the ringdown phase of black holes, however, is extremely challenging, as it requires solving highly-coupled and sometimes higher-order partial differential equations. We here extend a novel approach, \textit{Metric pErTuRbations wIth speCtral methodS} (METRICS), to study the metric perturbations and the quasinormal mode frequencies of ringing black holes in modified gravity. We first derive the asymptotic behavior of metric perturbations at the event horizon and spatial infinity for rotating black holes beyond general relativity. We then extend the eigenvalue-perturbation theory approach of METRICS to allow us to compute the leading-order modified gravity corrections to the quasinormal-mode frequencies and metric perturbations. We apply METRICS to rotating black holes in scalar-Gauss-Bonnet gravity. Without decoupling or simplifying the linearized field equations in this theory, we compute the leading-order corrections to the quasinormal frequencies of the axial and polar perturbations of the $nlm = 022$, 021 and 033 modes of black holes of $a \leq 0.85$. The numerical accuracy of the METRICS frequencies is $\leq 10^{-5}$ for $a \leq 0.6$, $\lesssim 10^{-4}$ for $0.6 < a \leq 0.7 $, and $\lesssim 10^{-2}$ for $0.7 < a \leq 0.85 $ for all modes studied. We fit the frequencies as a polynomial in spin, whose coefficients (up to second order in spin) are consistent with those obtained in previous slow-rotating approximations. These results are the first accurate computations of the gravitational quasinormal-mode frequencies of rapidly rotating black holes (of $a \sim 0.85$) in scalar-Gauss-Bonnet gravity.

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