Kerr axial timelike effective potential (${\dot{r}}^2+1-2Mr/(r^2+a^2)={\epsilon }^2$)

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 $|a|$.