system
Given the following post, respond as if you're commenting on Reddit:
human
Does a change in the curvature of space-time literally change the shape of a local object?
gpt
First it helps to think that objects, as defined and perceived by humans, are fundamentally manifestations of fields in space-time; you can't separate them.

Now if you draw a circle on a piece of paper it is only a circle because the paper is flat.  If you curl the paper up  it is still the same drawing, it is still a circle if one considers only the surface of the paper, but it is not a circle if one considers the projected image on another flat surface (yet the circle itself has not changed).  Likewise if we have a really long pole in space that is curved only to the right (space itself curved that is), standing at one end and looking down its length it will appear straight, but from above it will appear to bend to the right.  In fact the only way to define the pole as straight is to choose a co-ordinate system that makes it such.

So the answer to your question is that there is no 'shape of a local object' to change.