Paradox about black hole evaporation

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Discussion Overview

The discussion revolves around a paradox involving two characters, Jack and Jill, in the context of black hole evaporation and the nature of event horizons. It explores the implications of Jack approaching the event horizon of a black hole while Jill observes him from a distance, considering the effects of time dilation and the finite evaporation of the black hole.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Exploratory

Main Points Raised

  • Some participants propose that Jill sees Jack asymptotically approach the event horizon but never actually reach it due to time dilation effects, leading to a perception of him being "frozen" at the horizon.
  • Others argue that if Jack crosses the event horizon, he cannot return, and Jill's observations must be consistent with whether he crossed it or not.
  • A participant highlights the need to distinguish between events in spacetime and the signals that reach Jill, suggesting that the process of black hole evaporation alters the spacetime outside the horizon.
  • Some participants question the implications of Jack's constant speed and whether he can maintain it while experiencing gravitational forces, suggesting that if he is not free-falling, he may not be able to keep a constant speed.
  • There are differing views on whether Jill will see Jack cross the horizon at the same time the black hole evaporates, with some asserting that she will and others contesting this claim.
  • A participant mentions that Jill can only claim Jack was alive as he approached the event horizon, but once the black hole evaporates, she receives no further information about him.

Areas of Agreement / Disagreement

Participants express multiple competing views regarding the nature of Jack's approach to the event horizon and the implications of black hole evaporation. The discussion remains unresolved, with no consensus on whether Jill sees Jack cross the horizon or the implications of his journey.

Contextual Notes

There are unresolved questions regarding the definitions of speed in the context of black holes, the nature of signals emitted by Jack, and the changing spacetime due to black hole evaporation. The discussion also highlights the complexity of analyzing scenarios involving event horizons and time dilation.

  • #31
PeterDonis said:
That quantity is not limited to ##c##; it increases without bound as ##r = 0## is approached. So it cannot be interpreted as a "speed".

If you are fine with that, then I think the answer is that ##dr / d\tau = c## when the true event horizon is crossed, but I have not done the math to confirm that.
Thank you. (I used "speed" because it corresponds to Newtonian escape velocity, But I do not need to interpret it as "speed",just ##dr / d\tau## is ok.)
 
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  • #32
Found the paper by Ashtekar and Bojowald 2005. It is not very technical but has some references that surely need to be read in addition, but summarizes a lot of issues with the "traditional" semi-classical approach instigated by Hawking on BH evaporation.
 
  • #34
otennert said:
this is based on the assumption that the final naked singularity is spacelike

The singularity isn't naked since it's behind a horizon, but it is spacelike, yes, like the one for an eternal Schwarzschild black hole.

otennert said:
to me it is not really clear that this is the case. It is not even clear to me that a final singularity exists at all.

Yes, that's an open question. But this particular thread is discussing that model, since that's the setting for the OP's scenario.
 
  • #35
otennert said:
The discussion has evolved

You're the only one who is trying to do that. If you want to discuss the more general questions you are raising, please start a separate thread.
 
  • #36
The OP question has been answered, and this thread is closed.
 

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