The region beyond the ring singularity in the maximal Kerr spacetime is described as having closed timeline curves. Why and/or how is the question.
Now if you look a Kruskal-Szkeres Diagram (or a Penrose Diagram as above) you can see that the Kerr singularity (right) is timelike but the Schwarzschild singularity is spacelike.
Inside the Schwarzschild event horizon curves with constant longitude, latitude, and areal radius are actually spacelike so areal radius is actually a time direction. So you could claim that since r is the timelike direction there are curves that start and stop at the same t (since t is a spacelike direction) but I've never seen anyone claim there are CTC inside the event horizon of a Schwarzschild solution.
And even if we interpreted it like that, the region in Kerr where r (not areal r in Kerr, but the usual r for Kerr) is timelike is the region between the two horizons. And the lines making an X to the right of our universe are the outer horizon (see Penrose diagram) whereas the lines making an X to the left of the right most singularity is the inner horizon so the region between where r is timelike isn't connected to the singularity except in its infinite past (where we won't go).
So over where the singularity is, the singularity is a vertical line and is r=0 so r looks pretty spacelike there. We can avoid the singularity since that vertical line is r=0 which includes the whole disk that has the ring as its edge.
So we can get to the region the diagram labels as the weird space. And people usually just cite Hawking and Ellis for the existance of closed timelike curves instead of working it out but on page 164 the existence of closed timelike curves is asserted, but then it seems like it is just a discussion of the ergoregion and the two horizons, but I don't see any more mention of closed timelike curves until the section on Gödel's solution which is a different solution, not the Kerr solution.
So I'd like to know why and/or how there are closed timelike curves in the negative r region of the Kerr solution. And if someone knows why people cite Hawking and Ellis for that fact that would be interesting too.