I apologize for seeming to return on a same question, but I don't have the feeling that the things are clear.
In a former question, "where is the potential energy stored", the conclusion was that this energy is stored in the field of mutual interaction between two objects. But it seems to me that this conclusion doesn't arrange well with other facts.
To shorten the story, my question is : if an asteroid approaches the Earth, does it find the gravitational field of the Earth there, ready, or the field appears between the two objects?
The thing is analogous with a big electric charge A. When a point charge B is brought in the neighborhood of A, does B find the field of A ready or the field appears between the two bodies?
One should not let oneself eluded by the fact that the Earth is a big and the asteroid is small. If the Earth has around itself a field, so has the asteroid.
And, if possible, what kind of matter is the static field? A travelling field is photons, gravitons, neutrinos, other particles. But the static field? It contains energy, the energy is stored in matter.