Hollow planet with another planet inside it
I was wondering what would happen if there was a planet with a "shell" of stone entirely surrounding it (not connected, just held in place by gravity), with a few holes all the way through the outer shell, and two civilizations - one on the outside, and one on the inside. Would this be feasible? Would the outer shell need to be made of a specific material for it to work? Besides the fact that the outer civilization would likely suffer from droughts (as all the water flows into the interior), what consequences could this have on the two civilizations?
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Apart from the problems of formation and the problems of mechanical stability already mentioned by others, there's also the problem that gravitation cannot preserve that situation.
If the sphere were perfectly symmetric, then the sphere would neither feel a net gravitation from the planet, nor the other way round. Of course the shell would feel the planet's gravitation as stresses, but those would not affect the movement. The planet would not even notice the sphere.
If the shell were absolutely tight, one might speculate that the air is denser in the inside of the shell than on the outside, and thus the atmosphere in between would keep the two spheres concentric (since air pressure gets less with height, whenever one side of the shell gets closer to the planet, it gets larger pressure and thus gets pushed back; I admit I didn't calculate whether this really works out that way). However since your shell has holes, any difference between the inside and outside air would quickly equilibrate.
One thing that might work in theory is if the outer shell is superconducting, and is held in place by the magnetic field of the inner planet. However you'd have to assume that there's a material that's superconducting at the planet's temperature. Also, a shell out of such a material would probably not happen naturally; it therefore would need to be a constructed object.
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