Suppose one had a solid sphere just slightly larger than its Schwarzschild radius. What would the curvature of the surface look like to a local observer? Would it curve downwards, or appear flat, or curve upwards? If my brain was working a bit better today, I'd calculate it myself from the Schwarzschild metric or look for it in my old notes, but I'm just hoping someone can save me the trouble. I have a suspicion, without calculating, that it probably approaches being flat, as I think that the curvature of space matches that of the surface. (At the photon sphere, further out, the curvature of space plus that of space-time matches the surface).