Gravity in Hollow Shell: Nonadditivity and Relativistic Self-Interaction

[snorkack]

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?

 

[Ibix]

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.

 

[Matterwave]

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.