Quizatzhaderac wrote:↶Yes, it does. The coordinate acceleration adjusted for time dilation approaches to infinity. Otherwise, one would be able to escape the event horizon with a finite thrust. That's what the event horizon is, the point where not finite outward acceleration can cause you to escape.Eebster the Great wrote:As you fall into a black hole, your acceleration does not approach infinity from any perspective, at least not until you reach the singularity. The gravitational redshift does. Hawking radiation is not a result of this infinite redshift being cancelled out.

The thrust necessary to hover (or turn around) at a given height increases to infinity as you get closer to the horizon. The proper acceleration in freefall does not, because the falling observer's time is further dilated by moving at great speed.

I think you should try to work through the actual math on this one.Recessional velocity is proportional to proper distance. Since the free falling object distance is increasing, it's recessional velocity must be increasing to maintain that constant relationship; a change in velocity is an acceleration. As the falling object is accelerating relative to the center, and the frame is not, therefore there is an acceleration between the two. This is also true if we start from looking at the change in proper or comoving distance between the shell and the falling object.Why do you think the rigid cosmological horizon case experiences acceleration?

If the frame has been accelerated up to velocity Hd toward the center, so that d is no longer changing, then no further acceleration is needed to maintain proper distance. The fact that a bit of dust (comoving with the center of the sphere) moves away with increasing recessional velocity due to the accelerating expansion of the universe means no more to the local apparent acceleration of the frame than it does to us, in the center. (After all, we're stationary relative to ourselves, and the recessional velocity of distant galaxies increases over time, and yet we don't feel any acceleration as a result.)

From the perspective of the sphere, after the initial boost, dust is just something with a particularly high peculiar velocity that then, as it recedes, gets augmented by metric expansion. Just like cosmic rays that fly past us here on Earth.