Gravitation, 2 objects of same properties

[Destroxia]

Okay so I'm under the understanding that the way gravitation works is that each object warps the space around itself, and essentially objects caught in the warping are "falling" towards the object with the bigger warp in the center.

So my question is, how do objects that are complete clones of each other, that have the same mass and everything, fall towards each other? Wouldn't the space warps almost make a "mountain" of space between the two, like tectonic plates moving towards each other, and the objects would actually end up repulsing each other? Or as they near each other would their warps combine and just form a big bowl which the both of them fall towards each other at the same rate? Also, is there a distance at which gravitation will have a negligible effect? Or is the warping of spacetime seemingly infinite, decreasing it's slope infintessimally?

Thank you for your answer, also please correct me if I have any misconceptions about how gravity and the warping of space works, and if space actually warps the same as if a mass was placed on a fabric?

 

[A.T.]

Thank you for your answer, also please correct me if I have any misconceptions about how gravity and the warping of space works, and if space actually warps the same as if a mass was placed on a fabric?

Yes, that is a misconception. Read this:
https://www.physicsforums.com/threa...visualization-of-gravity.726837/#post-4597121

 

[Topolfractal]

You have a lot of questions. I will do my best to knock them out one by one.
2 identical objects move differently through each others spatial curvature depending on their initial velocity and position.
2 clones moving toward each other will collide and conglomerate into one body ( truly combining their warps)
2 clones orbiting around each other will orbit around their center of mass.
Now space is a lot more malleable than tectonic plates. Therefore no " mountain " between them can form. The curvatures just merge together. Picture an extremely tough rubber sheet and two equivalent bowling bowls rolling down to the center. Their respective curvatures are merged into the one of a body twice as big. Now the rubber sheet and bowling ball analogy is good but don't over extend it.
1. It doesn't include time
2. It doesn't include the third dimension
3. It is elastic deformation space can bend in a lot more ways without snapping.
Also yes space time asymptotically approaches Minkowski space time as one gets infinitely far away.