标题： 艾里函数方法处理二元黑洞合并波形：折叠焦散衍射模型 显示英文标题

标题： Airy-function approach to binary black hole merger waveforms: The fold-caustic diffraction model

摘要： 从爱因斯坦方程的数值模拟以及引力波观测来看，双黑洞合并产生的引力波信号被发现是简单且具有某些普遍特征的。 考虑到广义相对论的非线性在此过程中被认为起着重要作用，这种简单性显得有些出人意料。 这些普遍特征包括：随着我们接近合并点，振幅不断增加，在这里过渡到一个阻尼区域的模式似乎与初始条件无关。 我们提出了一种以Airy函数为基础的模式来模拟双黑洞（BBH）合并波形，重点在于解释其简单性和普遍性。 我们假设相关的普遍特征受以下物理机制控制：i) 在基本的“几何光学”近似下的焦散现象，ii) 在焦散上的衍射使其发散得到正则化。 焦散及其衍射图案的普遍性解释了所观察到的普遍特征，正如光学现象中的彩虹一样。 如果这一假设成立，那么我们可以借用奇点（灾变）理论的数学技巧，特别是Arnol'd-Thom定理，用折叠焦散来理解双黑洞合并。 对应于折叠焦散的衍射图案可以用Airy函数表示，这在“一致近似”的情况下导致了以参数化Airy函数形式写出的波形模型。 合并后的阶段并不具备相同的简单性和普遍性特征，必须单独加入。 然而，我们的提议允许通过已知的Airy函数渐近表达式实现旋进和合并后信号的平滑匹配。 显示英文摘要

摘要： From numerical simulations of the Einstein equations, and also from gravitational wave observations, the gravitational wave signal from a binary black hole merger is seen to be simple and to possess certain universal features. The simplicity is somewhat surprising given that non-linearities of general relativity are thought to play an important role at the merger. The universal features include an increasing amplitude as we approach the merger, where transition from an oscillatory to a damped regime occurs in a pattern apparently oblivious to the initial conditions. We propose an Airy-function pattern to model the binary black hole (BBH) merger waveform, focusing on accounting for its simplicity and universality. We postulate that the relevant universal features are controlled by a physical mechanism involving: i) a caustic phenomenon in a basic `geometric optics' approximation and, ii) a diffraction over the caustic regularizing its divergence. Universality of caustics and their diffraction patterns account for the observed universal features, as in optical phenomena such as rainbows. This postulate, if true, allows us to borrow mathematical techniques from Singularity (Catastrophe) Theory, in particular Arnol'd-Thom's theorem, and to understand binary mergers in terms of fold caustics. The diffraction pattern corresponding to the fold-caustic is given in terms of the Airy function, which leads (under a `uniform approximation') to the waveform model written in terms of a parameterized Airy function. The post-merger phase does not share the same features of simplicity and universality, and must be added separately. Nevertheless, our proposal allows a smooth matching of the inspiral and post-merger signals by using the known asymptotics of the Airy function.