Macroscopic objects in free-fall

[cianfa72]

But if the tidal effects are non-negligible, those non-geodesic paths will still result in a shape of the body that is different from what its shape would have been in flat spacetime in the absence of any geodesic deviation (i.e., spacetime curvature).

However, as you highlighted before, even in this case the body's COM continues to follow a geodesic path in free-fall.

 

[PeterDonis]

as you highlighted before, even in this case the body's COM continues to follow a geodesic path in free-fall.

Yes.

 

[pervect]

TL;DR: Analysis of macroscopic objects in free-fall in gravitational field

Hi,
very basic question. Take an object like a rock or the Earth itself. If we consider their internal constituents, there will be electromagnetic forces acting between them (Newton's 3th law pairs).

From a global perspective if the rock is free from external non-gravitational forces, then it will be in free-fall in gravitational field (i.e. spacetime geometry).

What about the aforementioned internal forces ? If we look at the center of mass (as object’s representative), then the electromagnetic internal forces driving the object’s costituents away from their geodesic paths will not enter into account, I believe.

It seems to me you are asking, at least in in part, about the self-force problem. "How does a particle, the thing that you are calling a constituent of your larger body, move taking into account the field it itself generates".

This is a simple question to which AFAIK we don't have a definitive fully satisfactory answer, even in electromagnetism. I gather we do have some less than complete answers and approximations, but I've never quite understood them.

Test particles without mass don't generate fields and don't have the self-force problem, they do follow geodesics. In general, things are messier and I don't know the answers, just that they're messy.