Perturbations of Spinning Black Holes beyond General Relativity: Modified Teukolsky Equation
Perturbations of Spinning Black Holes beyond General Relativity: Modified Teukolsky Equation
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DOI：
10.1103/physrevx.13.021029
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发表时间：
2022-06
影响因子：
12.5
通讯作者：
Dong-Yu Li;Pratik Wagle;Yanbei Chen;N. Yunes
中科院分区：
文献类型：
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作者：
Dong-Yu Li;Pratik Wagle;Yanbei Chen;N. Yunes
LIGO/Virgo合作探测到的引力波来自紧凑的双星合并，这是第一次允许在强，动态和非线性区域测试相对论引力。在爱因斯坦相对论之外，旋转黑洞可能与广义相对论中的黑洞不同，它们的合并可能会导致修改后的环缩。我们研究了后者，并首次导出了修正的Teukolsky方程，即，一组线性的，解耦的微分方程，描述了辐射纽曼-彭罗斯标量$\Psi_0$和$\Psi_4$的非克尔黑洞的动力学扰动。首先，我们专注于非里奇平坦，彼得罗夫D型黑洞的背景下修改的重力，并通过直接去耦和通过一种新的方法，提出了由Eschrasekhar，使用一定的规范条件，推导出修改Teukolsky方程。然后，我们将这种分析扩展到非Ricci平坦的，彼得罗夫I型黑洞背景在修改的重力，假设它们可以被视为一个线性扰动的彼得罗夫D型，黑洞背景在GR通过推广Ehrasekhar的方法，并推导出解耦的修改Teukolsky方程。我们的工作为在修正引力下研究任意自旋黑洞聚并的振铃相辐射的引力波奠定了基础。我们的工作也可以扩展到计算极端质量比的双螺旋在修改后的重力发射的引力波。
The detection of gravitational waves from compact binary mergers by the LIGO/Virgo collaboration has, for the first time, allowed for tests of relativistic gravity in the strong, dynamical and nonlinear regime. Outside Einstein's relativity, spinning black holes may be different from their general relativistic counterparts, and their merger may then lead to a modified ringdown. We study the latter and, for the first time, derive a modified Teukolsky equation, i.e., a set of linear, decoupled differential equations that describe dynamical perturbations of non-Kerr black holes for the radiative Newman-Penrose scalars $\Psi_0$ and $\Psi_4$. We first focus on non-Ricci-flat, Petrov type D black hole backgrounds in modified gravity, and derive the modified Teukolsky equation through direct decoupling and through a new approach, proposed by Chandrasekhar, that uses certain gauge conditions. We then extend this analysis to non-Ricci-flat, Petrov type I black hole backgrounds in modified gravity, assuming they can be treated as a linear perturbation of Petrov type D, black hole backgrounds in GR by generalizing Chandrasekhar's approach, and derive the decoupled modified Teukolsky equation. Our work lays the foundation to study the gravitational waves emitted in the ringdown phase of black hole coalescence in modified gravity for black holes of any spin. Our work can also be extended to compute gravitational waves emitted by extreme mass-ratio binary inspirals in modified gravity.