About the nature of gravity

Question

Let's consider a corner of spacetime far enough of any other mass so that the spacetime would be nearly flat in this neighborhood, a kind of mass desert. Let's consider a mass in the center of this nearly flat region of spacetime.

In the best understanding of gravity we have thus far, then this mass will curve the spacetime around it.

Is it correct to conclude that the gravity is an interaction between mass and spacetime and that there is no need for any other mass to experience gravity?

Then is it correct to consider that the newtonian gravity between 2 masses is the side effect of 2 interactions mass → spacetime and spacetime → mass as John Wheeler stated it? In the same way as 2 electrons seems to be attracted toward each other as a side effect of the attraction they both have toward the nucleus inside an He atom. When in fact there is not any attraction between the 2 electrons, it's exactly the opposite ( an illusion of attractive interaction hides an atractive and repulsive interaction ).

Answer 1

Is it correct to conclude that the gravity is an interaction between mass and spacetime and that there is no need for any other mass to experience gravity?

Yes! In this sense, General Relativity gives rise to self-interaction, something that doesn't exist in Newtonian gravity. This makes the equations non-linear and thus notoriously difficult to solve. So usually, we consider approximate solutions. When you want to describe a planet moving around a star, the curvature created by the planet will be negligable compared to the curvature created by the star (because it has a much larger mass). So to first order, you can assume that the space-time geometry doesn't change with time. Then, it becomes quite easy to determine the movement of the planet in this static environment.

Once you include the self-interactions (i.e. the curvature created by the planet itself), you will not be able to write down any solutions with pen and paper.

Then is it correct to consider that the newtonian gravity between 2 masses is the side effect of 2 interactions mass → spacetime and spacetime → mass as John Wheeler stated it?

Sure. One mass curves space-time and the other mass simply follows the shortest path in this new geometry. But it's not necessary for the interaction that both masses curve spacetime, if that's what you mean.

In the same way as 2 electrons seems to be attracted toward each other as a side effect of the attraction they both have toward the nucleus inside an He atom.

I'm not sure if this is a helpful analogy. There are still forces between the He atom and the individual electrons. In general relativity, gravity is not a force in the classical sense. A better analogy would be centrifugal force. When you are rotating, you feel a force acting on you, but this is simply an effect of your reference frame. Thus, we call it a ficticious force. You can think about gravity in the same way.