I'll have a go at defining it, term-by-term, > smooth Meaning no abrupt kinks (for a notion of abrupt which is probably not physically achievable, so don't wo

I'll have a go at defining it, term-by-term, > smooth Meaning no abrupt kinks (for a notion of abrupt which is probably not physically achievable, so don't worry to much about it) or jumps/discontinuities in the path of a particle, applying to both space and time > timelike roughly speaking, traveling slower than the speed of light > future-directed meaning going into the direction of causality > with intersections meeting itself again. In other words, it's a path through space/time on which you experience your own local time as always running forward, but yet somehow you end up in the past. Perhaps an analogy is in order. Suppose we were in 1+1 dimensions, with the time dimension being compact (closing in on itself). Visualize this as an infinite cylinder (the infinite axis being space). Now, let's impose a finite speed of light (for simplicity 1cm/s) and define the direction of causality, say counter-clockwise. Then, this spacetime has CTC, because we can find a path that, is smooth, future-directed (going around counter-clockwise) and timelike (going at angles < 45 degrees compared to the spacial axis). The simplest such would be a simple circle around the cylinder, but any curve that matches the above rules and intersects itself would be considered a CTC. Now, as a final note " a crude way of bringing out the fact that the application of familiar local laws of relativistic physics to a spacetime background which contains CTCs typically requires that consistency constraints on initial data must be met in order for a local solution of the laws to be extendable to a global solution." means the following. When we usually do physics, we know what happens locally (e.g. ball get shot at wall, bounces back), so we simply have to figure out (or decide if we're doing a thought experiment) where everything is in the universe at some particular time, apply our rules everywhere and we essentially know what's happening everywhere, anywhere. This doesn't work any more in the presence of CTC. "Consistency conditions" basically just means that you have to chose your placement of objects in such a way that they don't cause any paradoxes (there's a more technical notion here, but that's essentially what's meant).