Radial Schwarzschild escape with asymptotic speed
= Radial Schwarzschild escape with asymptotic speed
For asymptotic <speed> $0\le u<c$, $k=(1-u^2/c^2)^{-1/2}$ and the local outward <speed> obeys $v_{\rm loc}^2=u^2+(2GM/r)(1-u^2/c^2)$. It tends to $c$ as the horizon is approached from outside, though a static observer cannot actually remain on the horizon.