Re 'potential' - it seems that something underlies the 'reaction' of spacetime to mass. Is this in the 'time' component?

Also I wonder whether a 'potential' could be found in the way a volume expands. My elementary (elementary school?) understanding of the formula for the volume of a sphere (a 2-sphere, i.e. a common 'ball' shape?) leads me to wonder whether an expanding sphere (a 3-sphere?) ends up with potential, in that if you give the sphere the ability to expand by itself at a constant rate at its outer edge, you end up with less volume than you expect per expansion period.

So I guess I am wondering whether expanding spacetime could be described in such a way that the spacetime operates on itself to produce an effect of some kind, without having a mass involved.