[bermanoid]

It should also be mentioned that the reason why time travel is a problem is not merely that you can send a signal backwards in time, but that the signal may be used to then prevent the sending of the signal.

This is not necessarily a problem - in a quantum mechanical formulation, it's simple enough to resolve (for instance) a grandfather paradox by looking at quantum interference around causal loops (almost 100% analogous to the way interference on a violin string will restrict stable modes to certain frequencies, interference around a causal loop will only allow stable self-sustaining situations to survive, so any grandfather paradox would self-interfere and not be allowed). The main difference is that with closed timelike curves the quantum effects can get a lot stronger than without them, even affecting very large objects.

[jerf]

I was sticking to GR for simplicity.

[bermanoid]

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.