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(g) is the same size as the acceleration that the stationary observer needs
to have to keep from being in a free-fall frame. And at the horizon that
acceleration is infinite. Or another way to say it if you consider a
succession of constant r shells closer and closer to the event horizon,
approaching (mathematically) from the outside. A rocket that wants to stay
stationary will have to fire its engines (or else fall-in). the closer you
get to the horizon the "harder" your engines will have to fire, the larger
acceleration your rocket must have relative to the free-fall frame.
(e.g. for a rocket to hover 1 meter above the earth's surface requires it
to accelerate 9.8 m/s^2 relative to the free fall frame at that point.)
This acceleration must increase to infinity at the event horizon, as we know
that at the event horizon there is no acceleration that will prevent you
from falling in.