There is a very fundamental flaw in the common explanation given of the space-time curvature due to massive objects. It is said that a massive object curves space time just like a bowling ball on a rubber sheet, and another object near the massive object simply rolls down-hill on the rubber sheet, that is the reason why we observe that the other object is experiencing gravitational attraction to the massive object which curved the space-time.
The flaw is this:
Even if the massive object did bend the spacetime downwards, and there was a second object in the vicinity, this second object just would not roll down-hill automatically, unless there was a SECOND EXTERNAL source gravity, other than these two objects pulling everything downwards. In other words, even if the space time is curved, there is no particular reason for the second object to move closer to or be attracted by the first, because there is no other external force that would force it to move down-hill.
As a visualization, consider the bowling ball on a rubber sheet and another object on the same rubber sheet in outer space where there is no other source of gravity. Now, neither will the bowling ball curve the rubber sheet downwards (because it is not being pulled downwards), nor will the other object move down-hill on the rubber sheet even if the rubber sheet was depressed downwards, because there is no downward gravitational force from earth or another external source which would cause either of these two effects. So, there would be no reason for the other object to be attracted towards the first object. This is inconsistent with observation because objects do really experience gravitational attraction towards each other. But it certainly can't be explained by the bowlig ball and rubber sheet example. What is the explanation for all this?
Flaw 2: If there are 2 massive objects on the rubber sheet, they will both bend spacetime around themselves, and they will both remain trapped in their own depressions, and would never move towards or be attracted to each other. This is again contrary to observation. Since both masses are in reality attracted to each other, so they can't possibly bend spacetime and can't be trapped in their own depressions. Why?
Flaw 3: All pictures of bent spacetime on the web show spacetime being bent downwards. Why? In open space, with no other object nearby, all directions are equivalent to all other directions, and "downward" is undefined. So if spacetime is really bent, in which direction is it really bent?