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>A free falling observer is in an accelerating frame,
This is the big difference between how Newtonian mechanics treats gravity and how General Relativity treats it: a free-falling observer is *not* in an accelerated frame. In fact, that's what makes the fall free: there are no forces on the observer (since gravity is not a force in GR), so Alice and Bob are (after they jump) in inertial frames. Only Charlie, who stayed back on the ship, is accelerating.
Standing still on Earth as I am, I might seem to be at rest, and that's how I would think of it while doing a high-school physics experiment. But even according to Newton, I'm really in a revolving frame with a cycle of a day (actually one a bit more complicated than that). Similarly, Einstein treats me as inertial in his thought experiments with trains describing Special Relativity, but he knows (since he didn't write that stuff until after he came up with GR) that in reality I am (in addition to revolving) being constantly pushed away from Earth by the floor, as if in a great space elevator (which was another of his thought experiments).
A distant observer, watching me from space, would see me revolving, but they wouldn't otherwise see me accelerating (although they could infer it from their knowledge of gravity). However, if they get closer to Earth, certainly if they're close enough to get captured by Earth's gravity themself, then they'll see me (along with the rest of Earth) rushing towards them (if they're in free fall themself), and even accelerating. So accelerating objects can appear motionless from a distance, but up close you can observe the truth.
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