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I was reading about gravitational waves and about laser based detectors. I also read this. As mentioned in the answer, when ever there is a deformation in spacetime, doesn't it also create a minute time dilation? So in a laser based detector, even if the distance between the objects change when a gravitational wave passes, doesn't the time dilation affect the time taken by the laser to travel between the objects and make it a constant?

Edit

Later I read this What makes us think we can actually detect gravitational waves? as well. But I still think the time dilation argument makes sense.

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Sreekumar R
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1 Answers1

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Here is the metric of the gravitational waves in spherical coordinates (source):

$\eta_{\mu \nu} = \begin{bmatrix} -1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & r^2 & 0 \\ 0 & 0 & 0 & r^2 \sin^2\theta \end{bmatrix}$

As you can see, it changes only the space coordinates. And only the transversal ones. If there is a change also in the time coordinate, it is not a gravitational wave any more. So, the short answer in the literal sense is a clear no.

But, the gravitational waves are coming from the Einstein Field Eqations by calculating the metric far from the accelerating bodies. Somewhere I've read there are other wave-like gravitational effects with different metric, but they decay with higher powers with the distance from the source. Hopefully somebody with a higher understand in the topic will explain its details.

Extension: Fortunately it already happened in this wonderful answer.

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peterh
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