Quasinormal modes, echoes and the causal structure of the Green's function
Quasinormal modes, echoes and the causal structure of the Green's function
复制标题
格林函数的拟正态模式、回声和因果结构
DOI：
10.1088/1475-7516/2019/12/020
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发表时间：
2019
影响因子：
6.4
通讯作者：
Wong, Sam S.C.
中科院分区：
文献类型：
--
作者：
Hui, Lam;Kabat, Daniel;Wong, Sam S.C.
拟正态模式描述了扰动系统恢复平衡的过程，特别是黑洞合并的衰荡阶段。但作为全局定义的量，拟正规谱可能对全局结构高度敏感，包括对势的遥远小扰动。在什么意义上，准正规模式是由此产生的黑洞的属性？我们针对具有不相交有界支持的两个势的线性化扰动方程探索这个问题。我们给出了朗斯基矩阵的复合定律，它决定了组合系统的拟正规频率。我们表明，在短时间尺度上，演化是由个体势的准正常频率控制的，而对全局结构的敏感性可以用回声来理解。我们引入了格林函数的回波展开，并表明，正如一般意义上所预期的那样，在任何有限时间因果关系限制了可以贡献的回波数量。我们用一对 δ 函数势的可解示例来说明我们的结果。我们解释了格林函数的因果结构，证明了在什么条件下两个非常不同的准正规光谱会产生非常相似的振铃波形。
Quasinormal modes describe the return to equilibrium of a perturbed system, in particular the ringdown phase of a black hole merger. But as globally-defined quantities, the quasinormal spectrum can be highly sensitive to global structure, including distant small perturbations to the potential. In what sense are quasinormal modes a property of the resulting black hole? We explore this question for the linearized perturbation equation with two potentials having disjoint bounded support. We give a composition law for the Wronskian that determines the quasinormal frequencies of the combined system. We show that over short time scales the evolution is governed by the quasinormal frequencies of the individual potentials, while the sensitivity to global structure can be understood in terms of echoes. We introduce an echo expansion of the Green's function and show that, as expected on general grounds, at any finite time causality limits the number of echoes that can contribute. We illustrate our results with the soluble example of a pair of δ-function potentials. We explicate the causal structure of the Green's function, demonstrating under what conditions two very different quasinormal spectra give rise to very similar ringdown waveforms.