 Schwarzschild radial fall from rest at a finite radius

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