I think you don't really want to assume that your space-time is flat (both here and in your previous question) because of what Greg and Ryan said. Let me elaborate: in a non-inertial frame the speed of light might be non-constant and so the light cone might be curved, but still its projection onto the simultaneous hyperplane of the observer would be a homeomorphism. ("Simultaneous" from the viewpoint of an inertial observer who sits on the trefoil, and "projection" is along the lines of rest in the frame of that observer.) For that reason even the non-inertial observer would still see just a long trefoil in his light cone.
On the other hand, if you allow curved spacetime, then light cones may bend, but they still project homeomorphically onto the "horizontal" hyperspace - unless the observer is within the event horizon of a black hole. Things get more interesting if the poor observer did get into such a place. Then his light cone bends beyond the vertical line (=the line of rest in the absence of the black hole).
(Note: the picture shows the bending of future light cones.) Then the observer's past light cone is bent enough that it can surely happen to contain the closed knot that is the connected sum of a trefoil with its mirror image. In fact, you can almost see the connected sum of anything with its mirror image in this NASA picture of how sky would look from near a black hole:
I would think that in the case of one black hole and the trefoil outside the event horizon this is about all you can get: either a long trefoil or the closed connected sum of the trefoil and its reflection. As the observer approaches the event horizon from within (maybe not physically but in a thought experiment), the reflected trefoil goes off to infinity, ending up (just as the observer evaporates) with long trefoil in the limit. I have no idea how things might work with two black holes, one within the event horizon of the other.
If not only the observer but also the trefoil is within the event horizon, it is even more fun. (There is an issue however that if the trefoil is a physical rope it will not stay at rest in that position because of the black hole gravity.) Suppose that the observer is again moving towards the event horizon from within. Then he could see trefoil + mirrored trefoil in the beginning, and just a closed unknot in the end (because the light reflected by the trefoil would never reach him) still before he gets out of the event horizon. As he moves, he would have to observe a null-concordance of a trefoil. I find this to be pretty cool: just get inside the event horizon of a black hole, and you will see knot concordances with your eyes!
