The effect of gravitational waves in transverse traceless gauge on matter is represented by the expansion and contraction of a ring of test particles in the direction of polarization of the wave.
This result is obtained by choosing a gauge which in GR is a choice of a coordinates.
Does that mean that choosing another coordinate system(moving observers) would experiment time dilatation plus the effects of streching and contracting?
EDIT:
When the weak field approximation is used and the metric is split into $g_{ab}=\eta_{ab}+h_{ab}$ the gauge transformations are no longer coordinate transformations and instead define equivalence classes of symmetric tensors in the flat Minkowski background.
Then two Lorentzian frames are related by $h_{ab}=\Lambda_{a}^{\mu}\Lambda_{b}^{\nu}h_{\mu\nu}$, so uniform moving observers will measure time dilatations different from that of Minkoswki when the wave is passing.
Is this correct?
What about accelerated observers? Are there any extra effects in the full non-linear case?
Answer
Anywhere there is energy there is time dilation.
But you have used a linear approximation - which may hide the super - tiny effect of time change as a wave runs though a region of space.
In other words, if there was a beam of gravity waves, and one person was in the waves, the other not, the person who experienced the waves would have a small difference in their watch as compared to the person who was not in the wave zone.
For any realistic intensity of gravitational waves, the time dilation is likely not measurable using experimental techniques.
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