Aparently, I’ve conflated Level with Plumb, the walls cannot be parallel and plumb. Due to the curve, the center of gravity for the walls would require them to angle in slightly together or not be plumb.
The original post has nothing to do with the curvature of space time, or non-Euclidean geometry.
This only has to do with the fact that on a plane (e.g floor of a building, of literally any size), above a gravity source (here, we can treat the earth as a point source), the gravitational vector will only be perpendicular to the surface at a single point. All other points will experience gravity at an angle.
Yeah I realized that before I submitted it but it still sounded cool.
Also I’m not entirely convinced that the fact we can model and real-world gravitational mass as a point is entirely independent of the fact that gravity curves spacetime.
Like, we don’t have infinite sheets of gravitational material out in space. Gravity tends to clump material together into spheres and, for quickly-rotating masses, discs. What are those shapes other than equipotent shells drawn around that curved space?
