So what I can infer is that this all metric maths is nothing but to explain the gravity as produced by matter. But there is catch, not very deep also, the metric analysis says that the matter affects the geometry of spacetime as defined by metric. Ideally speaking maths should explain effect of X (real entity) on Y (another real entity), but in these theories the maths is explaining the effect of matter (real entity) on spacetime (mathematical tool) Now the spacetime also is a mathematical tool, so to define gravity the deformation of a mathematical tool is used. I see no link with maths directly touching upon the reality. It is maths working on a mathematical tool to explain the reality. Isn't it weird or is it our inability to associate spacetime with something real as on date. May be in near future we can comprehend that spacetime is much more than a mathematical abstraction.