双黑洞合并中的二阶和高阶准正规模
Second and higher-order quasi-normal modes in binary black hole mergers
摘要：
黑洞振荡是最重要的引力波源之一，也就是所谓的准简正模。我们建议，更高的微扰阶的QNM，产生的非线性引力相互作用的BH附近，是可检测的，值得寻找的观测和模拟的二进制BH合并。我们计算了二阶的度量扰动，并在视界和空间无穷远处明确地正则化了主方程。我们发现，二阶QNM的频率是一阶QNM的两倍，GW振幅是一阶QNM的约10%。QNM频率也将向蓝移高达~ 1%。这为广义相对论提供了一个新的检验，也是一个可能的距离指示器。
英文摘要：
Black hole (BH) oscillations known as quasi-normal modes (QNMs) are one of the most important gravitational wave (GW) sources. We propose that higher perturbative order of QNMs, generated by nonlinear gravitational interaction near the BHs, are detectable and worth searching for in observations and simulations of binary BH mergers. We calculate the metric perturbations to second-order and explicitly regularize the master equation at the horizon and spatial infinity. We find that the second-order QNMs have frequencies twice the first-order ones and the GW amplitude is up to ~10% that of the first-order one. The QNM frequency would also shift blueward up to ~1%. This provides a new test of general relativity as well as a possible distance indicator.
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