I was doing a little thought experiment and ran into a paradox. How to compute the gravitational field inside a spherical hole in a universe that is otherwise filled with uniformly distributed mass?
If we start with just a spherical shell of mass in an otherwise empty universe, then it is well-known that inside the shell, there is zero gravitation, independent of the thickness of the shell. If we then subsequently keep the inside of the shell the same size, but make the shell thicker and thicker, we should be able to make it fill the whole universe (assuming it is a spherically curved universe). By that reasoning, there should not be any gravitation inside a spherical hole inside a universe of equally distributed mass. So a small test mass near the border of the hole should not feel any gravitational force.
Now we subsequently fill the hole with a sphere of mass. The small test mass near the border of the hole should feel gravitation from this sphere of mass, that is just normal gravitation laws for spherical masses. If the test mass feels gravitation from the sphere, but not from the rest of the universe, then there should be a net gravitational force on it.
But if the hole is filled with a spherical mass of the same mass density as the rest of the universe, then effectively, there is no hole, and we just have a universe filled with uniformly distributed mass. In such a universe, the test mass should not feel any gravitation where ever it is placed.
Where does my reasoning go wrong, and how can the gravitation inside a spherical hole be calculated?