How does Schwarzschild space-time bend a free falling rigid body? Will it be stretched or squeezed? How much it will be modified? Can we find an effect of Lorentz contraction? When will the assumption of a rigid body be unphysical?
The geometrical shape of the rigid body is well-defined at infinity, which is asymptotically flat.
If we release a rigid body, with a certain shape, far away from the source of gravity with a certain initial condition, what can an observer see near the source?
As we say a rigid body, we accept that the interaction of the atoms inside is strong enough, with respect to the tidal force, so the distance between each atom remains a constant and the shape keeps unchanged.
What if we consider such a rigid body? Say, if it falls in radical direction? I would like to take the rigid body as a one dimensional rod with standard length as infinity, and I release it, I see it fall, and I ask my fellow near the source to measure the curved space in a radical direction... What if...
I came up with this question as I was learning General Relativity. I tried to ask my fellows around, but I don't have a reasonable answer. I don't know if this question is considered already. If so, could you please tell me where I can find the related discussion?