Greg Egan on Nostr: Your spacecraft is using its engines to stay a fixed distance from a black hole, when ...
Your spacecraft is using its engines to stay a fixed distance from a black hole, when your friend, who was taking a spacewalk, snaps their tether and falls towards the hole.
[This is a thought experiment where the hole is large enough that its tidal forces don't instantly kill anyone who gets close.]
If they are carrying a light, you will see it grow increasingly redshifted as they fall towards the event horizon, and they will appear to slow down. But at any given time for you, how far away will they “appear” to be?
Distances in curved spacetime are a slippery concept, but if we like, we can calculate a purely “apparent” distance: if we measure the parallax — the change in angle to the astronaut when observed at vantage points displaced to the left and right by a known baseline — we can ask what distance would produce the same parallax if everything was just sitting at rest in flat spacetime. So this is not in any sense “the true distance” to the astronaut; it is just a measure of how far away they look to us, based on the light rays we receive from them.
The red, green and magenta curves show how the apparent distance changes for you, if you decide to jump out of the spacecraft yourself after various delays. The two black dots on each curve mark the points where you would pass through the event horizon, and when you would hit the singularity.
[This is a thought experiment where the hole is large enough that its tidal forces don't instantly kill anyone who gets close.]
If they are carrying a light, you will see it grow increasingly redshifted as they fall towards the event horizon, and they will appear to slow down. But at any given time for you, how far away will they “appear” to be?
Distances in curved spacetime are a slippery concept, but if we like, we can calculate a purely “apparent” distance: if we measure the parallax — the change in angle to the astronaut when observed at vantage points displaced to the left and right by a known baseline — we can ask what distance would produce the same parallax if everything was just sitting at rest in flat spacetime. So this is not in any sense “the true distance” to the astronaut; it is just a measure of how far away they look to us, based on the light rays we receive from them.
The red, green and magenta curves show how the apparent distance changes for you, if you decide to jump out of the spacecraft yourself after various delays. The two black dots on each curve mark the points where you would pass through the event horizon, and when you would hit the singularity.