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I am not into general relativity, but the explanation of how an interferometric gravitational antenna works is generally pretty basic. In the recently published paper announcing the detection of gravitational waves we read:

[Advanced LIGO is] a modified Michelson interferometer (see Fig. 3) that measures gravitational-wave strain as a difference in length of its orthogonal arms. Each arm is formed by two mirrors, acting as test masses, separated by $L_x = L_y = L = 4~$km. A passing gravitational wave effectively alters the arm lengths such that the measured difference is $ΔL(t) = δL_x − δL_y = h(t)L$, where $h$ is the gravitational-wave strain amplitude projected onto the detector. This differential length variation alters the phase difference between the two light fields returning to the beam splitter, transmitting an optical signal proportional to the gravitational-wave strain to the output photodetector.

This neglects any possible effect that the perturbation of space-time can have on the light itself. In other circumstances, as gravitational lensing, this can be pretty evident.

I wonder if there exist corrections (eventually negligible), or if, what described in the paper, is actually the end of the story.

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