Proper acceleration of a static Schwarzschild observer
= Proper acceleration of a static Schwarzschild observer
A static observer at Schwarzschild radius $r>2M$ must maintain the outward <proper acceleration>
$$
a=\frac{M}{r^2\sqrt{1-2M/r}}.
$$
It approaches the Newtonian value $M/r^2$ at large radius and diverges at the horizon.