How Does Angular Momentum Affect Local Spacetime Curvature?

[rlance]

Homework Statement

t seems to me all momentum is angular momentum. An ice skater pulling in her arms will rotate faster, and obversely, extending her arms will slow her rotation. If her arms are extended to the radius of the planet, her rate of spin will slow to unnoticeable (to us), seeming instead to go in a straight line.

If as Einstein concluded, gravity and acceleration are indistinguishable, the spacetime curvature shown as gravity ought also to be observed as we shorten the arms of the ice skater from 4000 miles to 1 meter. She spins faster, and has a correspondingly more curved signature in her local spacetime.

So why aren’t other things close to her “sucked in” to her much more curved spacetime?

Homework Equations

The Attempt at a Solution

 

[Simon Bridge]

How do you know they are not?
Do the math and see.