= Solution
For nonzero $a$, $\Sigma=0$ requires $r=0$, $\theta=\pi/2$. Oblate Cartesian coordinates satisfy $x^2+y^2=(r^2+a^2)\sin^2\theta$, $z=r\cos\theta$, so this is the <Kerr ring singularity> of radius $|a|$. Curvature components and generic invariants diverge there. The whole $r=0$ surface is not singular: away from the ring it is a disk through which the extension continues to a sheet with $r<0$. This oblate radial parameter is not a nonnegative Euclidean distance.
In $G=c=1$ units, \b[$\boxed{J=Ma}$.] Horizon candidates solve $\Delta=0$, giving $r_\pm=M\pm\sqrt{M^2-a^2}$. For $J^2>M^4$, equivalently $|a|>M$, there are no real roots. \b[The over-rotating Kerr solution has no <event horizon> hiding its naked ring singularity.] The term <black hole> in this regime names the Kerr family, not a hidden-singularity <black hole>.
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