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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?

yess
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3 Answers3

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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.

Tom Andersen
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My rather limited understanding of GR is that for any vacuum region, Ricci scalar is zero. And that means, despite occasional comments from some GR authorities otherwise, gravity does not gravitate; i.e. is not a source unto itself. Hence gravitational field in general, whether owing to static source mass or presumed GW's, will not be equivalent to an actual stress-energy-momentum source as defined in the RHS of EFE's. Thus will not effect clocks - except possibly, in the GW case, in the SR sense of relative motional time dilation when two clocks are transversely separated and undergoing a rate-of-change-of-transverse displacement. But there are consistency issues with the very existence of so-called TT-gauge quadrupole mode GW's beyond the scope of this immediate issue.

user50679
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Oliver Heaviside showed in the end of the 19th century, that if the gravity field travels at a speed, then it behaves much the same way as the electric field: that is, magnetism is a consequence of the electric field travelling at a fixed speed, and likewise, co-gravitation or gravitomagnetism is a consequence of gravity of gravity travelling at a speed.

So if the effect sought happens with electromagnetism, it happens with gravity too, except that the gravity field is eighteen orders of magnitude less than electricity.

wendy.krieger
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