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New Consistency Relations between Averages and Variances of Weakly Lensed Signals of Gravitational Waves
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The lensing of gravitational waves (GWs) occurs when GWs experience local gravitational potential. In the weak lensing regime, it has been reported that a simple consistency relation holds between the variances of the magnification and phase modulation. In this paper, we present two additional consistency relations between the averages and variances of the weakly lensed GW signals in wave optics. We demonstrate that these consistency relations are derived as the weak lensing limit of the full-order relations for the averages of the amplification factor and its absolute square. These full-order relations appear to originate from energy conservation and the Shapiro time delay, and they are demonstrated to hold irrespective of the matter distribution.
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Consistency relations of amplitude and phase fluctuations of gravitational waves magnified by strong gravitational lensing
Consistency relations for GW amplitude and phase fluctuations remain unchanged when a strong lens is added to cosmological weak lensing, with second-order amplification and mean-signal magnification/Fresnel-scale shifts.
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