= Extremal Reissner-Nordstrom causal crossing
{c}
{title2=$\dot r^2=E^2-(1-M/r)^2$}
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.
Back to article page
