arXiv 2106.062092021-06gr-qcastro-ph.COastro-ph.HE

dCS引力场中慢转黑洞准正规模的解析计算

Analytical computation of quasi-normal modes of slowly-rotating black-holes in dCS gravity

Manu Srivastava, Yanbei Chen, S. Shankaranarayanan

备注：: v2: 19 pages, 2 figures, added a few references, version accepted in Phys. Rev. D
发表信息：: Phys. Rev. D 104, 064034 (2021)
DOI：: 10.1103/PhysRevD.104.064034

摘要：

利用引力波观测来寻找强引力区对广义相对论的偏离已成为一个重要的研究方向。Chern Simons（CS）引力是研究最多的宇称破坏强引力模型之一。已知克尔黑洞不是CS引力的解。与此同时，在动力学CS（dCS）引力的文献中唯一可用的旋转解是最精确地知道二次自旋的慢旋转情况。在这项工作中，对于慢旋转的情况下（精确到一阶自旋），我们推导出线性微扰方程的度规和dCS场精确到线性阶的自旋和二次阶的CS耦合参数（$α$），并获得准正常模式（QNM）的频率。在确认Wagle等人（2021）的最新结果后，我们发现在$α^2$的主要微扰阶上对本征频率校正的额外贡献。与Wagle等人不同，我们还发现对极扇区中的频率的校正。我们计算这些额外的修正，通过评估的期望值的微扰势的未微扰QNM波函数沿轮廓变形到复杂的$r$平面。对于$α=0.1 M^2$，我们获得在第一QNM频率（在极扇区中）中dCS校正与GR校正的虚部的比率为$0.263$，这意味着显著的变化。对于$(2,2)-$模式，dCS校正使得基模的第一QNM的虚部负性较小，从而降低衰减速率。我们的结果，以及未来的引力波观测，可以用来测试dCS重力和进一步约束CS耦合参数。[删节]

英文摘要：

Using gravitational wave observations to search for deviations from general relativity in the strong-gravity regime has become an important research direction. Chern Simons (CS) gravity is one of the most frequently studied parity-violating models of strong gravity. It is known that the Kerr black-hole is not a solution for CS gravity. At the same time, the only rotating solution available in the literature for dynamical CS (dCS) gravity is the slow-rotating case most accurately known to quadratic order in spin. In this work, for the slow-rotating case (accurate to first order in spin), we derive the linear perturbation equations governing the metric and the dCS field accurate to linear order in spin and quadratic order in the CS coupling parameter ($α$) and obtain the quasi-normal mode (QNM) frequencies. After confirming the recent results of Wagle et al. (2021), we find an additional contribution to the eigenfrequency correction at the leading perturbative order of $α^2$. Unlike Wagle et al., we also find corrections to frequencies in the polar sector. We compute these extra corrections by evaluating the expectation values of the perturbative potential on unperturbed QNM wavefunctions along a contour deformed into the complex-$r$ plane. For $α=0.1 M^2$, we obtain the ratio of the imaginary parts of the dCS correction to the GR correction in the first QNM frequency (in the polar sector) to be $0.263$ implying significant change. For the $(2,2)-$mode, the dCS corrections make the imaginary part of the first QNM of the fundamental mode less negative, thereby decreasing the decay rate. Our results, along with future gravitational wave observations, can be used to test for dCS gravity and further constrain the CS coupling parameters. [abridged]

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