I think this can be analysed in Schwarzschild coordinates for the interior.
Assuming that is correct, you can consider a trajectory in the Schwarzschild metric with dt = 0. Also take ds = 0 making the world line lightlike representing the limit of how fast they can go. Fix theta at pi/2. This gives a relation between dr and d(phi) which can be integrated as r goes from r_s down to zero. I did this and got the result delta(phi) = pi. If they both agree to move in the opposite direction they only need delta(phi) = pi/2 so they can comfortably meet up.
Even if they fall in at different times, the first in can almost hover just inside the horizon until the other one enters, so they can always meet up.
I am looking for a reference to confirm that this is right because I am certainly capable of getting it wrong.
Phil Gibbs
npub100…cc8sg
2025-10-27 13:35:08 UTC
in reply to nevent1q…fkgs
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wss://relay.momostr.pinkPublished at
2025-10-27 13:35:08 UTCEvent JSON
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"content": "I think this can be analysed in Schwarzschild coordinates for the interior. \n\nAssuming that is correct, you can consider a trajectory in the Schwarzschild metric with dt = 0. Also take ds = 0 making the world line lightlike representing the limit of how fast they can go. Fix theta at pi/2. This gives a relation between dr and d(phi) which can be integrated as r goes from r_s down to zero. I did this and got the result delta(phi) = pi. If they both agree to move in the opposite direction they only need delta(phi) = pi/2 so they can comfortably meet up. \n\nEven if they fall in at different times, the first in can almost hover just inside the horizon until the other one enters, so they can always meet up.\n\nI am looking for a reference to confirm that this is right because I am certainly capable of getting it wrong.",
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