= Minimum radius for radial turnaround with bounded proper acceleration
{title2=$g_{\rm hover}=GM/[r^2\sqrt{1-2GM/(c^2r)}]$}
For radial motion in <Schwarzschild spacetime>, $a^r=du^r/d\tau+GM/r^2$. At a prospective radial turning point $u^r=0$, bounded outward <proper acceleration> $g$ permits $du^r/d\tau\le g\sqrt{1-2GM/(c^2r)}-GM/r^2$. The equality $g=g_{\rm hover}$ defines a unique critical radius outside the horizon. A ship already falling inward cannot turn at or below it. The Newtonian proposed radius $\sqrt{GM/g}$ is strictly smaller and is therefore too late for reversal. A radius beyond the critical one is necessary, but braking must also remove the pre-existing inward <velocity>.
Back to article page
