Marginal escape geodesic in Schwarzschild spacetime
= Marginal escape geodesic in Schwarzschild spacetime
The outgoing radial <timelike geodesic> with zero <speed> at infinity has $k=1$ and $dr/d\tau=\sqrt{2GM/r}$. Thus $r(\tau)=[r_0^{3/2}+(3/2)\sqrt{2GM}\tau]^{2/3}$ and the local static-observer <speed> is $\sqrt{2GM/r}$.