 Solution

For $0<M<a$, the ring is a naked singularity and there is no event horizon shielding the extension's closed timelike curves. The weak cosmic censorship conjecture predicts that such superextreme Kerr geometries are not formed by generic collapse of regular isolated initial data satisfying the appropriate energy conditions. This is a conjectural physical restriction, not a proof from the exact metric alone.

For $M>a>0$, the closed timelike curves lie deep inside the ideal analytic extension, beyond the inner Cauchy horizon, so weak cosmic censorship does not itself exclude them. However, that inner horizon is unstable to perturbations, with mass inflation expected in realistic collapse. The strong cosmic censorship conjecture is the relevant obstruction to a regular continuation into the ideal chronology-violating region. Thus the exact Kerr extension exhibits such curves mathematically, but neither regular collapse nor the uniqueness theorem establishes that they occur in Nature.