We review the kinematic effects on a gravitational wave due to either a peculiar motion of the astrophysical source emitting it or a local motion of the observer. Working in the context of general relativity, we show at fully non-linear order in velocity, that the amplitude of the wave is amplified by the Doppler factor in the case in which the source moves with respect to a reference frame, while it is invariant if the observer moves (with respect to a reference observer). However, the observed specific intensity transforms in the same way under a boost of the source or of the observer. We also show at fully non-linear order that under a boost (of either source or observer), the polarization tensor is rotated in the same way the wave direction is rotated by aberration, such that the only net effect of a boost on polarization is to change the phase of the helicity components. We apply these results to a wave emitted by a binary system of compact objects in the cosmological context.

中文翻译：

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增强引力波：运动学对振幅、极化、频率和能量密度的影响综述


我们回顾了由于发射引力波的天体物理源的奇特运动或观察者的局部运动而对引力波的运动学影响。在广义相对论的背景下，我们以速度的完全非线性顺序表明，在源相对于参考系移动的情况下，波的幅度被多普勒因子放大，而如果观察者移动（相对于参考观察者），则波的幅度是不变的。然而，在源或观察者的推动下，观察到的比强度以相同的方式变换。我们还以完全非线性的顺序表明，在（源或观察者）的增强下，偏振张量的旋转方式与波方向的像差旋转方式相同，因此，增强对偏振的唯一净效应是改变螺旋度分量的相位。我们将这些结果应用于宇宙学背景下紧凑天体的二进制系统发出的波。