# Where is the CTC region of a Kerr Black Hole?

CTCs are found in the region where $$r < 0$$ . That should be just inside the ring singularity, since in Boyer Lindquist coordinate system $$r = 0$$ means ring singularity. Does that mean this image showing CTC outside the ringularity is wrong, or I am missing something?

https://www.researchgate.net/figure/This-is-how-light-cones-behave-in-Kerr-Newman-spacetimes-For-r-0-r-1-and-computations_fig2_1760606

You are missing something. In a text where $$r < 0$$ is possible, the singular ring is a curve, not a surface: its equation in B-L coordinates is $$(r = 0, \cos \theta = 0)$$.
In contrast, $$r = 0$$ is the equation of a surface: it consists of two disks $$(r = 0, \cos \theta > 0)$$ and $$(r = 0, \cos \theta < 0)$$ together with the singular ring, their common boundary. The 2 disks are made of regular points: they are actually 2 manholes through which you can reach into negative space.
The picture is ambiguous: if the text from which you got it claims the CTC is in negative space (not sure, the pic is clipped), then it lies below the region $$r = 0$$ rather than just outside.
• @Cham in such an interpretation, $r < 0$ is impossible. Dec 25, 2021 at 18:14