Greg Egan on Nostr: nprofile1q…ze5g0 The red/green/magenta curves are for increasing delays between the ...
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The red/green/magenta curves are for increasing delays between the first astronaut falling and the others falling, whose observations are plotted here.
The apparent distance they perceive the first falling astronaut to be when they cross the horizon is slightly larger as the delay gets longer. Of course if two people fell in very rapid succession you can make the distances they would measure between each other much smaller.
I would describe the 65.73M as much more an optical effect than a geometrical one — a kind of lensing. It is true that the Schwarzschild r coordinate is somewhat arbitrary (although not completely, since the proper-distance circumference of a circle of constant r is 2πr), but there’s a sense in which the proper distance to the horizon can be given an objective value that would put it at about 14 M.
The red/green/magenta curves are for increasing delays between the first astronaut falling and the others falling, whose observations are plotted here.
The apparent distance they perceive the first falling astronaut to be when they cross the horizon is slightly larger as the delay gets longer. Of course if two people fell in very rapid succession you can make the distances they would measure between each other much smaller.
I would describe the 65.73M as much more an optical effect than a geometrical one — a kind of lensing. It is true that the Schwarzschild r coordinate is somewhat arbitrary (although not completely, since the proper-distance circumference of a circle of constant r is 2πr), but there’s a sense in which the proper distance to the horizon can be given an objective value that would put it at about 14 M.