标题： 哪些引力透镜退化在波动光学中被打破？ 显示英文标题

标题： Which gravitational lensing degeneracies are broken in wave-optics?

摘要： 本文研究了引力透镜在波光学领域的退化问题，重点放在透镜化的引力波（GWs）上。 考虑透镜化退化为到达时间延迟曲面的重新缩放（或变换），我们可以将其分为局部和全局两种类型。 局部退化仅影响局部区域的时间延迟曲面，而全局退化通过一个常数重新缩放整个时间延迟曲面，同时保持各种观测到的图像属性不变。 我们表明，在波光学领域可以打破局部退化，因为透镜效应变得对总的到达时间延迟曲面敏感，而不仅仅是对图像位置处的时间延迟值敏感。 另一方面，全局退化（如相似性变换、棱镜变换和质量片退化）将放大因子乘以一个常数因子（比如说，$\lambda$）。 然而，在GW透镜中，由于GW信号幅度依赖于源距离，结果发现$\lambda$与哈勃常数完全退化，这类似于我们在几何光学中看到的情况。 因此，对于GW的透镜化，全局退化在波光学中像在几何光学中一样难以打破。 显示英文摘要

摘要： This paper studies gravitational lensing degeneracies in the wave-optics regime, focusing on lensed gravitational waves (GWs). Considering lensing degeneracies as re-scaling (or transformations) of arrival time delay surface, we can divide them into local and global types. Local degeneracies only affect the time delay surface in localized regions, whereas global degeneracies re-scale the whole time delay surface by a constant while keeping the various observed image properties unchanged. We show that local degeneracies can be broken in the wave-optics regime since lensing effects become sensitive to the overall arrival time delay surface and not only to the time delay values at the image positions. On the other hand, global degeneracies (such as similarity transformation, prismatic transformation, and mass-sheet degeneracy) multiply the amplification factor by a constant factor (let us say, $\lambda$). However, in GW lensing, as the GW signal amplitude depends on the source distance, it turns out that $\lambda$ is completely degenerate with the Hubble constant, similar to what we see in geometric optics. Hence, with the lensing of GWs, global degeneracies are as hard to break in wave optics as they are in geometric optics.