Does spacetime exhibit forces like tension in a bedsheet?

[nate808]

I know that Einstein said that gravity is the curvature of spacetime, but I'm a bit confused as to what happens as a massive body moves through space. When a body is in a certain position, it warps that area of space, but as it moves past that particular area, how does the area of space that was just previously warped move back into its original place. For example, people like to use the ball on a bedsheet example. The reason that the bedsheet moves back into its original position is due to the tension or pulling of the edges. Does spacetime exhibit such forces? I apologize if this question is trivial or dumb, but I was just curious.

 

[masudr]

The answer to the question you are looking for is fairly technically involved. Einstein's "equation" for GR is actually a set of 6 independent nonlinear partial differential equations all involving components of the metric to second order.

The solution to these explain all; including how a stress-energy tensor which behaves as though it moved in space over time will affect the components of the spacetime metric. I don't think anyone could give you a fairly simple answer; and although perhaps first-order effects are obvious, I don't see what they would necessarily be.

(A better word for spacetime would be timespace, but then convention is convention).

 

[pervect]

Spacetime really only "moves" in a very abstract sense. "Changes" would be a better word.

The best similarity between the "movement" of space-time and that of physical objects is the action principle. Both of these phenomenon obey a priniple of "least action". In the motion of matter, $\int L*dt$ is extremized - in GR, it's an intergal of the Ricci scalar, which comes from the curvature tensor, that's minimized.

The tricky part is determining how one talks about the evolution of "space-time" with "time" - whose time do you use?