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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?