Recently, the possibility of detecting gravitational wave echoes in the data stream subsequent to the binary black hole mergers observed by LIGO was suggested. Motivated by this suggestion, we presented templates of echoes based on black hole perturbations in our previous work. There, we assumed that the incident waves resulting in echoes are similar to the ones that directly escape to the asymptotic infinity. In this work, to extract more reliable information on the waveform of echoes without using the naive assumption on the incident waves, we investigate gravitational waves induced by a point mass plunging into a Kerr black hole. We solve the linear perturbation equation sourced by the plunging mass under the purely outgoing boundary condition at infinity and a hypothetical reflection boundary condition near the horizon. We find that the low frequency component below the threshold of the super-radiant instability is highly suppressed, which is consistent with the incident waveform assumed in the previous analysis. We also find that the high frequency mode excitation is significantly larger than the one used in the previous analysis, if we adopt the perfectly reflective boundary condition independently of the frequency. When we use a simple template in which the same waveform as the direct emissions to infinity is repeated with the decreasing amplitude, the correlation between the expected signal and the template turns out to decrease very rapidly.

中文翻译：

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由点质量坠入黑洞引起的引力波回波

最近，有人提出了在 LIGO 观测到的双黑洞合并之后在数据流中检测引力波回波的可能性。受此建议的启发，我们在之前的工作中提出了基于黑洞扰动的回声模板。在那里，我们假设产生回波的入射波与直接逃逸到渐近无穷远的入射波相似。在这项工作中，为了在不使用对入射波的朴素假设的情况下提取更可靠的回波波形信息，我们研究了由点质量坠入克尔黑洞引起的引力波。我们在无限远的纯出射边界条件和地平线附近的假设反射边界条件下求解由下沉质量产生的线性扰动方程。我们发现超辐射不稳定性阈值以下的低频分量被高度抑制，这与前面分析中假设的入射波形一致。我们还发现，如果我们采用独立于频率的完美反射边界条件，高频模式激发明显大于先前分析中使用的激发模式。当我们使用一个简单的模板，其中与无限远的直接发射相同的波形以减小的幅度重复时，预期信号和模板之间的相关性会非常迅速地下降。我们还发现，如果我们采用独立于频率的完美反射边界条件，高频模式激发明显大于先前分析中使用的激发模式。当我们使用一个简单的模板，其中与无限远的直接发射相同的波形以减小的幅度重复时，预期信号和模板之间的相关性会非常迅速地下降。我们还发现，如果我们采用独立于频率的完美反射边界条件，高频模式激发明显大于先前分析中使用的激发模式。当我们使用一个简单的模板，其中与无限远的直接发射相同的波形以减小的幅度重复时，预期信号和模板之间的相关性会非常迅速地下降。