# Gravity in Hollow Shell: Nonadditivity and Relativistic Self-Interaction

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• snorkack

#### snorkack

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?

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.

Ibix