= 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.
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