标题： 环下激励因子的重建 显示英文标题

标题： Reconstruction of ringdown with excitation factors

摘要： 在黑洞微扰理论框架下，引力波形式通过格林函数与辐射源项的卷积得到。因此，回响性质（即回响开始时间）依赖于这两个函数。格林函数中编码的未知时间偏移引入了“时间偏移问题”。我们通过重建旋转黑洞准正则模式（QNMs）的激发因子的波形来研究回响的时间偏移问题。首次重建了显著数量的带有激发因子加权的回响，并确认了其极佳的收敛性。然后我们精确地确定了回响的起始时间。我们还发现：(i) 对于中等或大自旋和 $\ell=m=2$，为了用不匹配阈值 $ M < O(10^{-3})$重建delta函数源的回响波形，需要包括到大约 $20$次前向过调和接近第五次后向过调；对于更高的角模态，需要更多数量的QNMs来重建它；(ii) 由格林函数引起的回响时间偏移对不同 $(\ell, m, n)$模态是一致的，但非平凡的源可能会改变这一结论。最后，我们演示了 (iii) 在频率域内可以通过叠加的QNM频谱重建灰体因子。 显示英文摘要

摘要： In black hole perturbation formalism, the gravitational waveform is obtained by the convolution of the Green's function and the source term causing radiation emission. Hence, the ringdown properties, namely its start time, depend on both functions. The unknown time-shift encoded in the Green's function introduces a "time-shift problem" for ringdown. We study the ringdown time-shift problem by reconstructing a waveform via the excitation factors of quasi-normal modes (QNMs) of a spinning black hole. For the first time, we reconstruct ringdown with a significant number of QNMs weighted with their excitation factors and confirm its excellent convergence. We then precisely identify the ringdown starting time. We also find (i) that for moderate or large spins and $\ell=m=2$, QNMs should be included up to around the $20$th prograde overtones and around fifth retrograde overtones to reconstruct the ringdown waveform for the delta-function source with a mismatch threshold $ M < O(10^{-3})$. For higher angular modes, a more significant number of QNMs are necessary to reconstruct it; (ii) that the time shift of ringdown caused by the Green's function is the same for different $(\ell, m, n)$ modes but that nontrivial sources can change this conclusion. Finally, we demonstrate (iii) that the greybody factor can be reconstructed with the superposed QNM spectrum in the frequency domain.