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?


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?

  • $\begingroup$ don't all objects return to the same height after a wave passes? they'd be desynchronized as the wave was passing, but the wave would affect them all equally, right? i don't know, i just wanted to contribute my two cents. $\endgroup$ – user40753 Mar 23 '14 at 1:03

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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  • $\begingroup$ If both are in the waves but moving from each other. Would they measure a time dilatation different that the one from Minkoswki? $\endgroup$ – yess Apr 5 '14 at 22:58
  • $\begingroup$ FWiW: there are pure radiation spacetimes that have manifest time dilation and that are exact solutions of Einstein's equations: en.wikipedia.org/wiki/Pp-wave_spacetime $\endgroup$ – Jerry Schirmer Jun 19 '14 at 17:10

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.

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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.

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    $\begingroup$ Electromagnetic fields don't distort time; gravitational fields do. $\endgroup$ – Peter Shor Mar 23 '14 at 14:41
  • $\begingroup$ Given that EM fields are a source of stress-energy-momentum, yes they do contribute (extremely weakly) to time dilation. Whereas a gravitational field per se will not. One has to distinguish between field as consequence of the true source which is any non-gravitational stress-energy-momentum, and field as a source in itself, which according to GR it is not. $\endgroup$ – user50679 Jun 24 '14 at 8:33
  • $\begingroup$ The effect of the co-gravitation is of the order of 120^-8 of gravity, because gravity does not have fast moving mixes of charges everywhere. Reading about co-gravitation, it is not necessarily a foregone conclusion that GR is correct in this manner. The idea of hiding behind quarterions does not help the case either, since not everyone is familiar with quarterions. $\endgroup$ – wendy.krieger Jun 24 '14 at 8:46
  • $\begingroup$ @PeterShor In my opinion, the answer describes gravitomagnetism as an analogy, i.e. which relates to gravitation as magnetism relates to electricity. The analogy doesn't mean equality in every sense. Your argument is like saying "effect of electromagnetic fields is proporitonal to the charge; gravitational fields not". $\endgroup$ – peterh - Reinstate Monica Aug 13 '16 at 10:05
  • $\begingroup$ @peterh: I don't believe this answer actually addresses the question. The OP seems to believe that Lorentz-shifting gravity waves results in something other than gravity waves of a different frequency. It doesn't. $\endgroup$ – Peter Shor Aug 14 '16 at 11:52

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