Eikonal quasinormal modes of black holes beyond general relativity. III. Scalar Gauss-Bonnet gravity
Eikonal quasinormal modes of black holes beyond general relativity. III. Scalar Gauss-Bonnet gravity
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超越广义相对论的黑洞的 Eikonal 拟正态模式。
DOI：
10.1103/physrevd.104.044051
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发表时间：
2021
影响因子：
5
通讯作者：
Glampedakis, Kostas
中科院分区：
文献类型：
--
作者：
Bryant, Albert;Silva, Hector O.;Yagi, Kent;Glampedakis, Kostas
在最近的一系列论文中，我们已经展示了程函/几何光学近似如何用于解析计算与波动方程耦合系统相关的基本准正规模频率，例如，在广义相对论之外的引力理论中黑洞扰动的研究中。作为这个系列的继续，我们在这里集中在标量高斯-邦纳引力假设一个小的耦合展开的非旋转黑洞的准正规模。我们表明，轴向扰动是纯粹的张量和修改后的Regge-Wheeler方程所描述的，而极性扰动是混合标量张量字符和描述的两个耦合波方程的系统。当应用到这些方程，程函机制导致轴向准正规模式偏离广义相对论的结果在二次阶的高斯-邦纳耦合常数。我们表明，这一结果是一致的分析不稳定的圆形零轨道黑洞在这个理论，使我们能够建立几何光学零测地线对应的轴向拟正规模式。对于极准正规模式，小耦合近似迫使我们考虑程函和小耦合微扰参数之间的顺序，其中之一，我们表明，通过明确的数值数据比较，产生正确的识别的标量张量耦合系统的波动方程的准正规模式。这些修正解除广义相对论简并标量和张量程函准正规模式之间的二次阶高斯-邦纳耦合的塞曼效应的方式让人想起。在一般情况下，我们的分析，程函准正规模频率（归一化到广义相对论的）同意与数值计算结果的误差在小耦合常数的制度。最后，我们发现，准正规模式的解析表达式是常见的一类广泛的标量-高斯-Bonnet理论领先的程函阶，显示非旋转黑洞，特别是标量-高斯-Bonnet理论在几何光学极限的准正规模式之间的退化。
In a recent series of papers, we have shown how the eikonal/geometrical optics approximation can be used to calculate analytically the fundamental quasinormal mode frequencies associated with coupled systems of wave equations, which arise, for instance, in the study of perturbations of black holes in gravity theories beyond General Relativity. As a continuation to this series, we focus here on the quasinormal modes of nonrotating black holes in scalar Gauss-Bonnet gravity assuming a small-coupling expansion. We show that the axial perturbations are purely tensorial and are described by a modified Regge-Wheeler equation, while the polar perturbations are of mixed scalar-tensor character and are described by a system of two coupled wave equations. When applied to these equations, the eikonal machinery leads to axial quasinormal modes that deviate from the general relativistic results at quadratic order in the Gauss-Bonnet coupling constant. We show that this result is in agreement with an analysis of unstable circular null orbits around black holes in this theory, allowing us to establish the geometrical optics–null geodesic correspondence for the axial quasinormal modes. For the polar quasinormal modes, the small-coupling approximation forces us to consider the ordering between eikonal and small-coupling perturbative parameters, one of which we show, by explicit comparison against numerical data, yields the correct identification of the quasinormal modes of the scalar-tensor coupled system of wave equations. These corrections lift the general relativistic degeneracy between scalar and tensorial eikonal quasinormal modes at quadratic order in Gauss-Bonnet coupling in a way reminiscent of the Zeeman effect. In general, our analytic, eikonal quasinormal mode frequencies (normalized to the General Relativity ones) agree with numerical results with an error ofin the regime of small coupling constant. Finally, we find that the analytical expressions for the quasinormal modes are common to a broad class of scalar-Gauss-Bonnet theories to leading eikonal order, showing a degeneracy between the quasinormal modes of nonrotating black holes in particular scalar-Gauss-Bonnet theories in the geometrical optics limit.
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