= Schwarzschild radial fall from rest at a finite radius
{c}
{title2=$r=\tfrac{r_0}2(1+\cos\eta),\quad s=\sqrt{r_0^3/(8M)}(\eta+\sin\eta)$}
For radial timelike <geodesic> fall released from rest at $r_0>2M$, the <Killing energy> is $E=\sqrt{1-2M/r_0}$ and the <proper time> radial equation is $(dr/ds)^2=2M/r-2M/r_0$. The displayed parameterization integrates its inward branch, with $s=0$ at release. The <Schwarzschild event horizon> is reached at $\eta_H=\arccos(4M/r_0-1)$ in finite proper time, even though <Schwarzschild time> diverges.
// Target: general-relativity.bigb
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