Kerr axial analytic extension ($d{s}^2=-Fd{t}^2+d{r}^2/F,F=1-2Mr/(r^2+a^2)$)

The two-dimensional symmetry-axis restriction of the Kerr metric has simple horizons at $r_{\pm }$ for $0<|a|<M$, but is regular at $r=0$ because the ring is off-axis. Its static region below the inner horizon continues to an asymptotically flat end at negative infinity. The horizon blocks repeat in the maximal analytic extension. This ideal continuation is distinct from a claim of physical stability at the Cauchy horizon.

Conserved stationary energy and unit timelike normalization give this equation in the Kerr axial analytic extension. For $a>0$, the negative-sheet maximum of the potential is $1+M/a$ at $r=-a$. Energy squared above this maximum permits an inward orbit to pass through regular $r=0$ and continue to negative infinity without a turning point. At energy squared one, zero is a turning point. For negative spin the threshold is expressed with $|a|$.