# How does Schwarzschild spacetime bend a free falling rigid body?

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?

• Commented Apr 26, 2022 at 12:35
• Rigid bodies are problematic even in special relativity, giving rise to the concept of Born rigidity en.wikipedia.org/wiki/Born_rigidity In general relativity Born rigidity seems to be trickier; my impression is that the research here is ongoing. Still, the behaviour of the 1D rod sounds like a good case where things might be more answerable. Commented Apr 26, 2022 at 18:32
• It is not very clear what you are asking, because you give the answer in the conditions of your question, “the distance between each atom remains a constant and the shape keeps unchanged”. So locally the shape is unchanged and your fellow there reports only the length contruction due to velocity. You however also observe the gravitational length contraction in the radial direction. In your coordinates, the rod quickly becomes a flat spot on the horizon, except invisible due to the infinite redshift. Commented May 6, 2022 at 18:53