A sphere contains all the mass on one side while the other side is empty of matter. Both sides are separated by a strong material, you name it, that will keep the sphere together. Given that the mass side is more massive than the sun or at least very massive, how would it behave in respect to gravity? Would it spin?
If the sphere is rigid, meaning it cannot change size or shape at all, then gravity will have no effect. Specifically, the sphere will not rotate.
The distances between all parts of the sphere are fixed, so the gravitational potential, which depends only on these distances, cannot change. Therefore there is no way for the sphere to release any gravitational energy and so it cannot move.
If the sphere is not rigid, it may be able to move some, and will oscillate in its normal modes of oscillation. However, due to conservation of linear momentum, the sphere can't go anywhere, and due to conservation angular momentum, it cannot rotate.