This question is primarily for publius, because it's a pretty gnarly general relativity issue, but anyone with insight on the issue is encouraged to chime in.

General relativity is a nonlinear theory, so you cannot say that the gravitational effect of 10⁵⁷ protons will be the same as 10⁵⁷ times the effect of one proton (as Newton would have it). But in simpler versions of GR, you can still get to the 10⁵⁷ proton gravity by adding up all the protons but modifying them for their potential interaction with each other, like subtracting their binding energy. This sounds rather like a "correspondence principle", where the theory that we would imagine applying to just one or a few protons would simply accumulate to a large number of them, in bottom-up fashion even if it wouldn't be the sensible way to do it.

But what if we have a rapidly spinning neutron star? My impression is, things are so complicated there that you'd have a hard time building that up one atom at a time, but rather you need to do it "holistically" with the full mass and all the required information in there right from the get-go to use the exact formalism of GR. But I don't know if that's true-- the stress-energy tensor is built up additively, so if it only depends on that, it has a correspondence principle. Similarly with the angular momentum. But does the exact result depend only on these additive entities? A black hole has "no hair", so is built from additive entities, but what about a neutron star? I guess the way to say this is, let's say you know the current neutron star gravity and spin, and so forth. Now add a single particle with a known rest mass, energy, and angular momentum. Can you calculate the new gravity of the neutron star exactly? Or do you need to specify more information than you can track from the particle you are adding-- in other words, is there an exact correspondence principle in general relativity?

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People think the problem with models is that they are limited by our minds, but the greater problem is that our minds are limited by our models.