What Causes Spacetime to Return to Uniformity?

[cosmonium]

so i am somewhat new to the theory of general relativity but in none of the papers i have read does anyone seem to explain what causes matter to attract... for example, the moon and the Earth are attracted to each other because each of them warps spacetime around themselves. these warped pockets could be thought of as low density areas in spacetime. Einstein says they attract because they are following the curvature of spacetime but what drives that motion? the only thing i can think of that would cause objects to want to clump together in a spacetime field is if spacetime is somehow elastic. it is as if for whatever reason there is a pressure-like force causing spacetime to want to return to a uniform distribution. is there a term for such a force and if so what causes it?

 

[Dale]

Einstein says they attract because they are following the curvature of spacetime but what drives that motion?

Inertia. GR says that gravitational motion is inertial motion.

 

[cosmonium]

interesting... could you expand on that? assuming 2 perfectly stationary objects in space that have are held in place for a long period of time (so any gravitational waves have already passed by) and then released, what about their inertia causes them to slope down the spacetime curvature?

 

[Ibix]

You need to generalise velocity to the four-dimensional equivalent, the four-velocity. This is never zero; it always has length 1 in geometric units. For the case of a stationary (in the 3d sense) mass, you can interpret this (probably slightly loosely) as saying that it is only moving through time. But spacetime is curved. So once your masses are released, their inertial paths are curves - which is to say that their velocity vectors rotate and the masses acquire spatial motion.

You'll need to learn up to connection coefficients and the geodesic equation to get a rigorous explanation of that.

 

[Dale]

interesting... could you expand on that? assuming 2 perfectly stationary objects in space that have are held in place for a long period of time (so any gravitational waves have already passed by) and then released, what about their inertia causes them to slope down the spacetime curvature?

Are you aware that on a sphere a great circle forms a "straight line" aka "a geodesic". If so, consider two nearby longitude lines. They are geodesics, and they are parallel at the equator but intersect at the poles.