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ldunn | 9 months ago

I agree that if you are freely falling and then you are suddenly not freely falling because you hit the surface of a planet and experienced a huge acceleration, you will notice. That doesn't have anything to do with anything I said, but it is undeniably true.

An event horizon is not like the surface of a planet - you will not be accelerated as you pass through it.

It is, once again, irrelevant that light cannot propagate outward once you're behind the horizon because, again, you are falling towards the center, and in particular you are falling through the future light cone of your feet. Please look at some spacetime diagrams if you do not believe me, preferably ones in Kruskal-Szekeres coordinates.

In GR spacetime is locally flat and for an inertial observer special relativity applies, up to tidal corrections which can be made arbitrarily small at the horizon by considering a suitably large black hole. This is a deep and important fact about GR. The idea that falling through the horizon causes you to suddenly not be able to see your feet anymore appears to obviously violate this basic principle, so if you think your assertion is true you should be able to explain why either this principle of GR is actually not true, or why your assertion does not actually violate this principle.

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bencyoung|9 months ago

Well, I disagree. Light literally can't move in a direction that makes it further from the singularity once inside the event horizon. I don't see what space being flat or not locally has to do with that. Check https://en.wikipedia.org/wiki/Event_horizon#/media/File:BH-n... for an example.

If your head is further from the singularity than your feet then you can't see them.

Happy not to discuss further!

ldunn|9 months ago

It doesn't have to move in such a direction! Look at a spacetime diagram and think about the trajectory of your head and feet! Read a book on GR! Do literally anything except have strong opinions about GR when you don't know any GR!

mr_toad|9 months ago

I was considering a stationary observer inside the event horizon, but that’s not possible. ldunn is correct that a free-falling observer will catch up with the photons reflected from their feet.

Space being flat locally is important because if the gravitational gradient is too high (i.e. you get too close to the singularity) your feet will be accelerated much faster than your head.