I’ve heard that IIRC if you have two people fall into a black hole such that they are just out of reach of each other, due to the way that geometry in the black hole works, they will forever stay out of reach for their entire fall, instead of getting close to each other. Is this correct?
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If they are in free fall then yes due to tidal forces and the resulting spaghettification, but if they have rockets they can still accelerate towards each other, they can pick velocities between -c (effectively the fastest) and -∞ (effectively the slowest, in terms of proper time), see here where you can replace the photons with strong ultrarelativistic rockets.
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$\begingroup$ Why are you still using this misleading animation representing the singularity as a point” when it is an infinitely long spacelike coordinate line? The animation also is misleading in that it shows the observers crossing the horizon at different times, which is unphysical. The flaw here is in assuming that the raindrop coordinates use the proper time of the falling observer, but this is not really true. On the proper clock of each of the two observers, the other crosses the horizon at the same time with him. While mathematically correct, physically this animation is meaningless. $\endgroup$ Commented Jul 6, 2023 at 4:31
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$\begingroup$ @safesphere - Feel free to make a better one, no one is keeping you from writing your own answer. $\endgroup$– YukterezCommented Jul 6, 2023 at 5:10
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$\begingroup$ I'm assuming a supermassive black hole here, tidal forces are low initially. $\endgroup$ Commented Jul 17, 2023 at 13:00
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$\begingroup$ @blademan9999 - the only reason they can be out of reach of each other are tidal forces, otherwise we'd have Minkowski and everything could reach everything else. $\endgroup$– YukterezCommented Jul 17, 2023 at 17:37
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$\begingroup$ Except no thrust is allowed. $\endgroup$ Commented Jul 18, 2023 at 2:03