论文标题
painlevé-II二进制黑洞合并动态的方法：可集成性的普遍性
Painlevé-II approach to binary black hole merger dynamics: universality from integrability
论文作者
论文摘要
二进制黑洞合并波形既简单又通用。通过对动力学的有效渐近描述，我们旨在从基础（有效）可集成结构方面考虑这种普遍性。更具体地说，在``波均流动''的角度下，我们建议与观察到的波形相对应的快速自由度将受到有效的线性动力学的影响，并在缓慢发展的背景下传播，以（有效）非线性集成动力学。后者的疼痛特性将根据所谓的painlevé-ii超越，在灵感阶段中提供i）轨道（尤其是emri）动态之间的结构联系，ii）ii）非线性分散式korteweg-de vries name serger（namey she nam name name nam kort）的自我相似溶液， iii）与后期响头动力学中黑洞准正常模式的同一特征相匹配。此外，Painlevé-II方程还提供了一个“非线性转折点”问题，在最近引入的二进制黑洞合并波形的通风方法中扩展了线性讨论。在提出的集成性视角下，二进制黑洞合并波形的简单性和普遍性将由基础可集成（有效）动态的“隐藏对称性”解释。本着渐近推理的精神，并考虑了沃德的猜想，将整合性和自dum-yang-mills结构联系起来，质疑这种通用模式是否会反映出（自dual）一般可靠性的（自dual）扇形的实际完全集成性，最终负责二进制黑洞波形模式。
The binary black hole merger waveform is both simple and universal. Adopting an effective asymptotic description of the dynamics, we aim at accounting for such universality in terms of underlying (effective) integrable structures. More specifically, under a ``wave-mean flow'' perspective, we propose that fast degrees of freedom corresponding to the observed waveform would be subject to effective linear dynamics, propagating on a slowly evolving background subject to (effective) non-linear integrable dynamics. The Painlevé property of the latter would be implemented in terms of the so-called Painlevé-II transcendent, providing a structural link between i) orbital (in particular, EMRI) dynamics in the inspiral phase, ii) self-similar solutions of non-linear dispersive Korteweg-de Vries-like equations (namely, the `modified Korteweg-de Vries' equation) through the merger and iii) the matching with the isospectral features of black hole quasi-normal modes in late ringdown dynamics. Moreover, the Painlevé-II equation provides also a `non-linear turning point' problem, extending the linear discussion in the recently introduced Airy approach to binary black hole merger waveforms. Under the proposed integrability perspective, the simplicity and universality of the binary black hole merger waveform would be accounted to by the `hidden symmetries' of the underlying integrable (effective) dynamics. In the spirit of asymptotic reasoning, and considering Ward's conjecture linking integrability and self-dual Yang-Mills structures, it is tantalizing to question if such universal patterns would reflect the actual full integrability of a (self-dual) sector of general relativity, ultimately responsible for the binary black hole waveform patterns.
