How Does Angular Momentum Affect Local Spacetime Curvature?

AI Thread Summary
Angular momentum significantly influences local spacetime curvature, as demonstrated by the example of an ice skater who spins faster when pulling her arms in, which theoretically increases the curvature of spacetime around her. According to Einstein's principle that gravity and acceleration are indistinguishable, this increased curvature should affect nearby objects. The discussion raises a question about why other objects are not drawn into this more curved spacetime. The response suggests that one must perform calculations to determine the actual effects of this curvature on nearby objects. Ultimately, the relationship between angular momentum and spacetime curvature warrants further mathematical exploration.
rlance
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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?

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The Attempt at a Solution

 
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