System for a zero-combat dungeon crawl?

[Beneath]

Basically the reason you can violate causality w/ faster than light is because for things only reachable by faster than light, sequence is undefined (relativity of simultaneity); in other words, if the distance between event A and event B is greater than c times the time between them in any reference frame, then (it is in all reference frames and) an inertial reference frame traveling at a velocity less than c exists where event A happens first, event B happens first, and they happen simultaneously (this is called "spacelike separation" because there is no reference frame where they happen at the same place; the opposite, timelike separation, has a defined sequence but in some reference frame they happen at the same place. the cusp between the two is lightlike separation, where the distance is exactly ct).

From this you can get that if you have a faster-than-light drive that does not have a preferred reference frame (i.e. whatever speed it sends you at, you can go at that speed in any arbitrary reference frame), you can take a round trip and arrive before you left.

A simple way to imagine this in two dimensions, let's use x for space and y for time in ground control's reference frame. Your ship points in some direction within 45 degrees of the y axis (the further off the axis it points, the faster it's moving), and you have an FTL drive that travels vast distances in an instant, in ship time (arrival and departure are simultaneous in the ship's reference frame). Your reference frame's "simultaneous" is the line perpendicular to the way your ship is pointing (remember, your FTL drive works on ship time, not ground control time). The math isn't exactly right here because in some cases you need a skew operation where I'm using a rotation but the principle works out.

Thus you accelerate to a high velocity, teleport to a nearby black hole, fall into a parabolic orbit, reverse your direction, and teleport back. Do this right, and you can arrive before you left. Seeing your doppleganger, you then arm and launch torpedos, shooting them down so that they can't then go back in time and murder your past self.

Did you complete the trip and shoot down your past self before you left, or were you shot down before you left, preventing you from shooting yourself down and thereby freeing you to complete the trip? Relativity does not hand you alternate timelines to play with; everything happens in one universe.

This is one of the points where relativity is weird and unintuitive, because it relies on relativity of simultaneity which is completely outside our everyday experience (in everyday life, speeds are slow enough that relativistic effects are negligible and we can sort-of assume a preferred reference frame); there's a good wikipedia article on that

Closed timelike curves become theoretically possible whenever you allow for spacelike travel, but it may be possible that you can't get any with a specific arrangement of a finite number of distinct wormholes (you can make a closed timelike curve with one, but if you're trying to get rid of them you probably can. If nothing else, you can all make them totally coincidentally more or less follow a preferred reference frame). Even the quoted article says that if you get FTL you get causality violations.