Comment by yshklarov

You are correct if you mean a 2-sphere, but a spherical shell in space-time would be a 3-sphere, which gives quite a lot more information. To make things a bit simpler we could consider a 2-sphere × an interval -- the boundary of a 4-dimensional cylinder -- which is to say, your spherical shell at all points in time from t_0 to t_1, and also the entire interior of the spatial region at both the initial time t_0 and the final time t_1.