 Extremal Reissner-Nordstrom causal crossing

A neutral radial timelike geodesic of an extremal black hole has conserved specific energy $E=(1-M/r{)}^2\dot{t}$, giving the displayed radial equation. An infalling geodesic reaches $r=M$ with finite nonzero $\dot{r}=-E$ and finite proper time. In ingoing coordinates, outgoing radial null curves have $dr/dv=(1-M/r{)}^2/2$; those starting inside approach $r=M$ only at infinite $v$ and cannot return to the same exterior future null infinity. This distinguishes causal access from length on a static slice, and supplies an operational event horizon test even without strictly trapped round spheres.