> It's pretty clear GP was using the reference frame of a far-away observer. Even in such a frame (for example, Painleve coordinates), not all of the statement

> It's pretty clear GP was using the reference frame of a far-away observer. Even in such a frame (for example, Painleve coordinates), not all of the statements are correct. In those coordinates, the infaller's coordinate acceleration is nonzero, as you say, but their coordinate speed inside the horizon is greater than the speed of light. Their inertial mass is still unchanged. And the coordinate acceleration in this frame is still not "towards" the singularity, since the singularity is still a moment of time, not a place in space. > It's totally fine to say 'a astronaut in freefall is accelerating towards the earth', explicitly invoking Earth's reference frame. In terms of coordinate acceleration, yes. But coordinate acceleration, precisely because it is frame-dependent, is not considered a physically meaningful quantity in relativity. Only invariants can be physically meaningful quantities. Proper acceleration--what an accelerometer attached to the infaller reads--is an invariant, and that is zero for a free-faller.