Gravitational waves on rigid bodies

Question

I have a question on gravitational wave (GW) detection.

I would assume that gravitational waves do not impact rigid bodies. I mean, GWs should be extremely weak with respect to electromagnetic forces that binds together atoms and molecules, thus rigid bodies should be completely "untouched" by GWs, a part for very extreme cases (i.e., black hole collision much nearer to the earth).

This kind of reasoning is the very same that one finds when talking about expansion of the universe: the expansion of the universe does not cause the earth (or any rigid body) to expand, because the "force" of the expansion is ridiculous low with respect to other forces (electromagnetic bonds or even the gravitational pull of the sun).

If this is true, then I don't understand why, when talking about LIGO GW detection, people always talk about "stretching" of the arms: the earth should not be affected by GW passing. In my understanding, the stretching would be of the space, but not of physical objects, thus it would e.g. affect the mirrors if they are somehow "detached" by the earth and free of moving in the space, but I don't know if this is the case.

If this is not true, and GWs do stretch the earth and rigid objects, I would expect that the amount of the stretching depended on the type of matter that the object is made of: I mean, GW impacting on wood sticks would have a different impact than on steel sticks. Thus the amount of stretching detected in one of the LIGO detectors would be different than the one in the other (because the soils have different compositions): Is this the case?

Answer 1

The mirrors at the ends of LIGO's arms have been mounted in such away that their motion along the direction of arms is (almost) completely decoupled from their physical surroundings. The motion of mirrors in LIGO in these directions can thus be considered in perfect free fall, and is thus susceptible to effects of passing gravitational waves.

When speaking about the stretching of LIGO's arms, people are not referring to the any actual stretching of the vacuum tubes, but to the stretching of the "empty" space between the mirrors. It is also worth keeping in mind that the actual change in path length between the mirrors due to a passing gravitational wave is less than the width of a proton!

Answer 2

The mirrors in a gravitational wave interferometer are a good approximation to inertial test masses. Their "connection" to the Earth, via the points from which they are suspended, is almost non-existent, thanks to $13+$ orders of magnitude of damping at the frequencies of the gravitational waves.

Answer 3

It depends on the GW frequency. If the GW frequency is well above the resonant frequency of the solid object, the stress will not accelerate the object's parts rapidly enough for the object to respond. So, the object will experience a time-varying internal stress because it is getting longer and shorter as the GW passes.

If the GW frequency is low compared to the resonant frequency, the object will simply respond by staying the same size. But accelerometers on different parts of the object will record different accelerations, as this does not correspond to geodesic trajectories for all parts of the object.

And, in resonance, the wave may excite a substantial oscillation of the body. This is the principle behind the Weber Bar.