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I have been studying about the gravitational wave memory effect from these papers:

1: https://arxiv.org/pdf/1705.01378.pdf

2: https://arxiv.org/abs/1003.3486v1

Now, it is evident that gravitational radiation travels along null lines to approach the null infinity. The null coordinates in the Brinkmann form of plane gravitational waves are denoted by U,V in the reference (1) that I have mentioned. The memory effect is defined by permanent shift in freely falling geodesics as a function of U(null line) at infinite past to infinite future.

But while I am observing at LIGO there is an inherent time coordinate that is associated with the graph of the strain versus time which ultimately measures the D.C nature of this entire effect. So my question is what exactly is the 'time' that is given in reference (2)(or what is the clock assigned to asymptotic observers measuring memory effect in practical experiment at LIGO) in the entire setting of the memory effect that is being observed along the null 'U' direction of gravitational radiation?

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