I'm thinking about a flat sheet-like structure approaching a massive object (maybe a black hole?). If it were to approach with the plane of the object tangent to the mass, it seems to me that eventually, with enough gravity, the sheet would end up looking much like those hokey "bowling ball on a sheet" illustrations of a gravity well. The tidal forces would spagettify the central portion of the object, while the outer areas would remain relatively uncurved, all proportional with the gravitational force affecting the various regions of the sheet-like object. So here's what I am unsure about: If an astronaut aboard the sheet-like craft were to sight down the long surface of the craft near the middle, would the craft look uncurved to the astronaut? Would photons from the far side travel along the curved surface and strike him in the eye? All as if the craft were still in a region of comparatively flat spacetime? If so, that is pretty cool. If not, why not?