We consider gravitational wave (GW) sources with an associated electromagnetic (EM) counterpart, and analyze the time delay between both signals in the presence of lensing. If GWs have wavelengths comparable to the Schwarzschild radius of astrophysical lenses, they must be treated with wave optics, whereas EM waves are typically well within the approximation of geometric optics. With concrete examples, we confirm that the GW signal never arrives before its EM counterpart, if both are emitted at the same time. However, during the inspiral of a binary, peaks of the GW waveform can arrive before their EM counterpart. We stress this is only an apparent superluminality since the GW waveform is both distorted and further delayed with respect to light. In any case, measuring the multi-messenger time delay and correctly interpreting it has important implications for unveiling the distribution of lenses, testing the nature of gravity, and probing the cosmological expansion history.

中文翻译：

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透镜引力波的表观超光度

我们考虑重力波（GW）源与相关的电磁（EM）对应物，并分析存在透镜时两个信号之间的时间延迟。如果GW的波长可与天​​文学透镜的Schwarzschild半径相媲美，则必须使用波光学器件对它们进行处理，而EM波通常在几何光学器件的近似范围内。通过具体示例，我们可以确认，如果GW信号同时发射，则它们永远不会在EM对应信号之前到达。但是，在吸入二进制数据期间，GW波形的峰值可能会在其EM对应物之前到达。我们强调，这只是表面上的超亮度，因为GW波形相对于光既失真而且进一步延迟。任何状况之下，