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I was sticking to GR for simplicity.



Right on, and I'm with you there - causality violation is a nasty nasty thing in physics, and causes all sorts of problems.

Even in GR, you can sort of allow causality violations if you're talking about field theory, but it's not pleasant; the problem is that the usual existence/uniqueness proofs (things like "If a solution to the field equations exists on some spacelike slice of spacetime satisfying a bunch of conditions, then there exists a (maybe unique) solution if that spacelike slice is carried forward in time", roughly speaking) usually rely on strong causality assumptions, and for instance it's pretty easy, depending on the situation, to come up with initial field configurations that have no solutions as they're swept forward because of closed timelike curves further along the manifold.




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