Typically, when discussing superluminal signaling in flat spacetime (specifically, how particles travelling faster than the speed of light can travel backwards in time in the frame of reference of a particular observer), spacetime diagrams are drawn as seen in this post and in Figure 1 of this paper, in order to visualize the situation. I was wondering how to extend this in the case where your observers are no longer in flat spacetime. Say, for example, Alice and Bob are spacelike separated and situated on either end of a traversable wormhole in an asymptotically flat spacetime, and they are sending superluminal signals to each other through the wormhole. Are there references in the literature that discuss this sort of situation, and how one would go about drawing a spacetime diagram for this?
I am also seeking to understand whether or not certain rules that prevent superluminal signaling in flat spacetime also hold in curved spacetimes. For instance, this paper argues that if superluminal signaling were to exist in Minkowski space, the nonlinearity of quantum mechanics would be violated (i.e., it would be possible to clone quantum states). Another paper argues that the fact that spacelike separated observables commute in flat spacetime eliminates any possibility of information being communicated faster than light (assuming that quantum theory and QFT hold true). Are there any references that discuss whether or not these rules still hold in a curved spacetime?
