Title: Probing Binary Lens Caustics with Gravitational Waves: A Uniform Approximation Approach Show Chinese title

Title: 通过引力波探测双星透镜晕环的统一近似方法

Abstract: We present a new framework for modeling gravitational wave diffraction near fold caustics using the Uniform Approximation (UA), focusing on binary mass lenses - axially asymmetric systems with complex caustic structures. Full-wave methods based on the Kirchhoff integral become impractical in this regime due to highly oscillatory integrands. The UA provides a robust and accurate description of the wave field near folds, resolving the breakdown of Geometrical Optics at caustics and improving upon Transitional Asymptotics - based on Airy function approximations - which lack global validity. Central to our approach is the concept of the caustic width, $d_c$, a characteristic length scale defining the region where diffraction significantly alters wave propagation. We find that $d_c$ scales universally with the gravitational wavelength as ~ $ \lambda^{2/3}$ and inversely with the redshifted lens mass as ~ $ M_{Lz}^{-2/3}$. The wave amplification near the fold grows as ~ $ d_c^{-1/4}$, substantially enhancing the signal and potentially playing a key role in the detection of gravitational waves lensed near caustics. Notably, for lens masses below the galactic scale, the caustic width for gravitational waves is not negligible compared to the Einstein radius - as it is in electromagnetic lensing - making the UA essential for accurately capturing wave effects. Show Chinese abstract

Abstract: 我们提出了一种新的框架，使用均匀近似（UA）来建模折叠奇点附近的引力波衍射，重点研究二元质量透镜——具有复杂奇点结构的轴向不对称系统。 基于基尔霍夫积分的全波方法在这一领域变得不切实际，因为积分核高度振荡。 UA 提供了对折叠附近波场的稳健且准确的描述，解决了奇点处几何光学的失效问题，并优于基于艾里函数近似的过渡渐近方法——后者缺乏全局有效性。 我们方法的核心概念是奇点宽度$d_c$，这是一个特征长度尺度，定义了衍射显著改变波传播的区域。 我们发现$d_c$与引力波长呈 ~$ \lambda^{2/3}$的比例关系，并与红移后的透镜质量呈 ~$ M_{Lz}^{-2/3}$的反比关系。 折叠附近的波增强增长为 ~$ d_c^{-1/4}$，显著增强了信号，并可能在靠近奇点的引力波透镜探测中起到关键作用。 值得注意的是，对于小于银河尺度的透镜质量，引力波的奇点宽度与爱因斯坦半径相比并不微不足道——这与电磁透镜不同——因此 UA 对于准确捕捉波效应至关重要。