Nonadditive gravity in a hollow shell?

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  • Thread starter snorkack
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  • #1
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Classical gravity is additive.
Therefore classical gravity obeys Gauss´ law. One result is absence of gravity in any hollow, spherically symmetric shell.

In general relativity, gravity is not additive.
Simple example is a black hole.
The gravity of a classical point mass diverges to infinity at zero distance, and the field flux is conserved. The gravity of a black hole diverges to infinity at a nonzero distance, and the field flux also diverges to infinity.

But the gravity of any mass distribution is nonadditive and the flux increases inwards.

Now, how does the relativistic self-interaction of gravity field work inside a hollow shell (that is not massive enough to be a black hole)? Does the field still cancel inside?
 

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  • #2
Ibix
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Yes. Birkhoff's theorem says that the only spherically symmetric vacuum solution to Einstein's field equations is Schwarzschild's. And that only depends on the enclosed mass.
 
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  • #3
Matterwave
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If the hollow shell is not moving then Ibix's answer applies - Birkhoff's theorem says the interior metric is Minkowski. If the hollow shell is rotating though you will get a Lense-Thirring effect (frame dragging). That's the level (for this scenario) at which GR would depart from Newtonian predictions.
 
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