I think you agreed with the fact that , gravity ( or force-field ) exists around a mass .
While gravity is modeled as a field and does represent a force between two objects, it is not accurate to call it a "force field". To do so you would first have to describe the mechanism through which gravity acts between two objects.
GR is currently our best explaintion of gravity and even GR does not really explain how mass and space interact such that space is curved, resulting in what we experience as gravity. It only says that they do and predicts the effect of the force between two objects.
While we can say that given two objects there is some gravitational force that exists between them, we cannot say that there is any "force" of gravity where only a single object is involved. We must have two objects whether they are galaxies, stars, planets or even particles. We cannot describe gravity as we currently experience it as a force field.