Bob and Alice - can Alice save Bob from the black hole with a very long pool skimmer?

Question

If Bob is in free-fall but close to the event horizon, and appears frozen to Alice, who is stationary at a much farther distance, and Alice were to extend a very, very long pool net and try to scoop Bob away, what would be her perception of the end of the net? She would observe her own actions in proper time, and manipulate the net fairly easily (let's assume she's very, very strong, and can keep her end of the pool net in place). But what would she see at the "net" end of the pool net, as she tries to scoop and rescue Bob? Would she see blurred movement, like when your screen freezes and the mouse pointer blurs as you move it?

The second part to this is, can Bob actually be rescued? For instance, would Bob really even be there, or would there merely be an image of Bob (because light would take so long to reach Alice), making rescue impossible. Thanks!

score 1 · Answer 1 · answered Nov 17 '19 at 06:12

Given that Alice is far away, and that she already sees Bob near the horizon, it's too late for her to help him even in principle.

Event horizons move outward at the speed of light (or faster); that's why they are one-way surfaces. Here's a spacetime picture of the situation in Kruskal or similar coordinates:

  black hole    /AAA
  interior     /AAA  <-- Spacetime region Alice can reach after seeing light
              /AAA
 horizon --> /AAA
            /AAA
           /  A  <-- Alice sees light                 Λ
        B /  .A                                       |  time
        B/  .A                                        |
        B  . A
       /B .  A 
      / B. <-- light emitted by Bob
     /  B

The event of Bob crossing the horizon is never in Alice's absolute past (unless she crosses the horizon too), but it also isn't in her future. Bob could in principle save himself at the last attosecond, which Alice hasn't seen yet. But she can't help him do it.

score 1 · Accepted Answer · answered Nov 18 '19 at 07:11

The geodesic chart below plotted in the Schwarzschild coordinates of physical space and time shows that the observer (Bob) in a free fall appears to Alice to be slowing down near the horizon (the blue curve). She sends a flash of light in his direction (the reddish curve). This light also slows down at the horizon in her coordinates. On this diagram, her light catches up with Bob (at the red arrow) only after he has crossed the horizon (that is never for Alice).

This example shows that, after a certain time, even light sent by Alice cannot reach Bob outside the horizon. Obviously, her pool net cannot move faster than light, so she can do nothing to save him.

She can save him only if she is close enough, starts moving her pool net soon, and moves it faster than Bob falls. The pool net would be under a lot of stress by the tidal forces and the force of Alice. She would see the net end with a delay and moving slower than she pushes her end (no blur). She also would see the pool net shorter than it actually is due to the radial distance contraction described by the Schwarzschild metric. And this rescue may take a long time for Alice, but less for Bob due to gravitational time dilation.

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Bob and Alice - can Alice save Bob from the black hole with a very long pool skimmer?

2 Answers2