TobyBartels on Nostr: (2/3): As we approach the black hole, we see our astronauts' spaceship, and at first ...

(2/3):

As we approach the black hole, we see our astronauts' spaceship, and at first (except when Alice and Bob jump in) everything appears motionless. But as we approach and get captured by the black hole ourselves, we realize that the ship is rushing towards us, accelerating even (which explains its rocket fire). And the event horizon seems to be accelerating towards us too. As we fall closer, the apparent speed of both the ship and the event horizon increases, but only as we pass them do we observe their true proper acceleration. The ship is accelerating just as much as it would be if the black hole were a planet like Earth, with the ship sitting on it, being pushed by the planet's surface.

As for the event horizon, as we pass it, we finally observe its true motion, which is at the speed of light. So it's actually not accelerating at all, but it's also moving faster than we were able to observe from outside. If we regarded the event horizon as at rest, then we would think that we ourselves were moving at lightspeed! So the event horizon cannot be at rest relative to any local inertial observer; anyone who sees it thus must be some combination of distant and accelerating, since they can't be travelling at lightspeed themself.

(2/3)