Suppose I construct a metal triangle in flat space the sum of the interior angles will be 180°. If I then move the structure into a curved space in which the sum of the interior angles of the triangle will be greater then 180° do the corners of my triangle experience stress? Or, do I simply measure a wider angle at each corner in the curved space because that is the nature of the space. Thinking this through I have 2 conflicting lines of reasoning... 1. If the corners of the structure experience stress they will flex. Now I have a force acting through a distance so work has been done to the structure. Where did it come from? If the triangle and I start out in flat space and I push it toward a region of curved space then the work must come either from the KE that I put into it when I pushed it or from the stress-energy that is curving the space. The first possibility would violate conservation of momentum. The second I can't wrap my head around well enough to determine if it's plausible yet. 2. If I simply measure a wider angle at each corner because that is the nature of the curved space, how do I measure it? If I take a protractor into the curved space along with my triangle wouldn't the same thing happen to my protractor that happens to my triangle, thus the correlation between a corner of triangle and a mark on the protractor would not change.