Why does the curvature of spacetime cause matter to experience gravity?
I’m familiar with the usual rubber sheet metaphor used to explain how space curvature causes gravity, but I’d like a more realistic understanding. In the rubber sheet metaphor, a rubber sheet is stretched out horizontally and two spheres are placed onto the sheet. The weight of the spheres indents the rubber, creating slopes in the sheet that are angled down towards a point between the spheres. The slopes result in the spheres rolling down and towards each other as if there were a force pulling them together. I’ve always found this explanation to be inadequate since the attraction experienced by the spheres is not dependent solely on the geometry of the rubber sheet. In addition to curvature, the metaphor requires an external force to pull the spheres “down” against the sheet is so that the spheres will actually move and follow the sheet’s curvature. If that external force was not there, even if you somehow granted the spheres the ability to curve the rubber sheet in the same way, the
