Pikkugnome said:
What is the difference between the GTR vacuum and the vacuum of quantum theory?
You've labelled this thread as B-level, but it's really an A-level question. Here's my attempt at an answer that's somewhere in between...
In flat (Minkowski) spacetime there's no difference between those vacua -- because QFT is constructed with Special Relativity as a foundation.
In any specific QFT, one constructs the (Fock) state space in terms of field modes (e.g., by a Fourier decomposition).
In a curved spacetime, it turns out that such a decomposition "here" (and the state space spanned by those field modes) is inequivalent to a (superficially similar) decomposition "there". In other words, the 2 state spaces are
inequivalent -- in general one cannot express the vacuum (or any other mode) in one of those state spaces as a linear combination of modes from the other. One must use more advanced techniques to handle this (Birrel & Davies is the classic reference).
So the short (probably still puzzling) answer to your question is that, in curved spacetime, there is an infinity of inequivalent versions of the simplistic vacuum of ordinary (non-interacting) QFT.
If you really want to know more, google for "Bogoliubov transformation". (Alas, you'll need to become proficient in ordinary QFT first, for this to make much sense.)